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23  WIST  MAM  STIHT 
|,N.Y.  14SM 
(7U)  •79-4903 


CIHM/ICMH 

Microfiche 

Series. 


CIHIVl/ICJVIH 
Collection  de 
mi 


Canadian  Instituta  for  Historical  IMicroraproductions  /  institut  Canadian  da  microraproductions  historiquaa 


Technical  and  Bibliographic  Notes/Notes  techniques  et  bibliographiques 


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une  image  reproduite,  ou  qui  peuvent  exiger  une 
modification  dans  la  mAthode  normale  de  filmage 
sont  ind(.'«u6s  ci-dessous. 


D 


Coloured  covers/ 
Couverture  de  couleur 


I      I    Covers  damaged/ 


Couverture  endommag6e 


Covers  restored  and/or  laminated/ 
Couverture  restaurAe  et/ou  pellicuMe 


Cover  title  missing/ 

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Encre  de  couleur  (i.e.  autre  que  bleue  ou  noire) 

I     I   Coloured  plates  and/or  illustrations/ 


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Reli6  avec  d'autres  documents 

Tight  binding  may  cause  shadows  or  distortion 
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mais,  lorsque  cela  Atait  possible,  ces  pages  n'ont 
pas  AtA  filmAes. 

Additional  comments:/ 
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D 
D 
D 
D 
D 
D 


D 
D 


Coloured  pages/ 
Pages  de  couleur 

Pages  damaged/ 
Pages  endommagtes 

Pages  restored  and/or  laminated/ 
Pages  restaur6es  et/ou  pellicuMes 

Pages  discoloured,  stained  or  foxed/ 
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Ce  document  est  film*  au  taux  de  reduction  indiquA  ci-dessous. 

10X  14X  18X  22X 


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16X 


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2SX 


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The  last  recorded  frame  on  each  microfiche 
shall  contain  the  symbol  -^  (meaning  "CON- 
TINUED"), or  the  symbol  y  (meaning  "END"), 
whichever  applies. 

Maps,  plates,  charts,  etc.,  may  be  filmed  at 
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1 

2 

3 

L'exemplaire  filmA  fut  reproduit  grflce  i  la 
gin^rositA  de: 

Library  of  Congress 
Photoduplication  Service 

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conformity  avec  les  conditions  du  contrat  de 
fllmage. 

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papier  est  imprimte  sont  fiimte  en  commengant 
par  le  premier  plat  at  en  terminant  soit  par  la 
dernlAre  page  qui  comporte  une  empreinte 
d'Impression  ou  d'illustration,  soit  par  le  second 
plat,  salon  le  cas.  'I'ous  les  autras  exemplaires 
originaux  sont  f  ilmte  en  commenpant  par  la 
premiere  page  qui  comporte  une  empreinte 
d'Impression  ou  d'illustration  at  en  terminant  par 
la  dernlAre  page  qui  comporte  une  telle 
empreinte. 

Un  des  symboles  suivants  apparaftra  sur  la 
dernlAre  image  de  cheque  microfiche,  selon  le 
cas:  le  symbols  — ►  signlfie  "A  SUIVRE",  le 
symbols  V  signlfie  "FIN". 

Les  cartes,  planches,  tableaux,  etc.,  peuvent  Atre 
filmte  i  des  taux  de  rMuctlon  diffirents. 
Lorsque  le  document  est  trop  grand  pour  Atre 
reproduit  en  un  seul  clichA,  II  est  filmA  A  partir 
de  Tangle  supArieur  gauche,  de  gauche  A  droite, 
et  de  haut  en  bas,  en  prenant  le  nombre 
d'images  nAcessaire.  Les  diagrammes  suivants 
lllustrent  la  mAthode. 


32X 


1 

2 

3 

4 

5 

6 

THK  PLANET  JUnTKB. 
Aa  »emt  with  thq  M-indt  telewope  at  WMblngton,  187B,  Jw  H 


/ 

AMERICAN  SCIENCH  SERIES,  BRIEFER  COURBS. 


ASTRONOMY 

SIMON   NEWCOMB,  LL.D. 

SUPBRINTKHDEyr  AMEHw'A    MPnSMSRia    AND  NAUTICAL  ALMASAO 


AND 


EDWARD    S.   HOLDEN,  M.A. 

DtBECTOR   OF  TUB    WASIIBUHN   OBaSRVATOBT 


h^ 


\v: 


s^ 


V-,  N-.V-       ^--^.   -i  ^^^        '.>•-. 


NEW  YORK 
HENEY  HOLT  AND  COMPANY 


i,jim«M- 


fl 


CopyriKht,  18M 

BY 

Hbmrv  Holt  &  C!a 


/ 


PREFACE. 


The  present  treatise  i«  a  condensed  edition  of  the  AHronomy  of 

J Lerican  Science  Series.    The  boolc  bus  not  been  shortened  by 

eavtg  out  anything  that  ^vas  essential,  but  by  omitt.ng  son.e  of  the 

ZZ  of  practical  astronomy,  thus  giving  to  the  descni,tive  por- 

tions  a  greater  relative  extension. 

The  most  marked  feature  of  this  condensation  .8  perhape.  the 
om^ln  of  most  of  the  mathematical  formula  of  the  ^^^^-^^^^ 
The  present  work  requires  for  i»s  understanding  only  a  ^a-  acquain 
ance  with  the  principles  of  algebra  and  geometry  and  a  slight 
knowlX  of  elementary  physics.  The  space  which  has  been  gained 
irtU  e^issionshas  Ln  utilized  in  giving  a  fuller  discuss.on  oj 
L  more  elementary  parts  of  the  subject,  and  m  treatmg  the  funda- 
mental principles  from  various  points  of  view. 
A  familiar  and  secure  knowledge  of  these  «  essential  to  the 

studerrealprogress.    The  ^"" '-'"  ^f  ^-^ J!:: uUde 
a  referencebook  to  a  student  who  has  studied  it  and  put  it  aside. 

Is  in  the  larger  work,  the  matter  is  given  in  two  sizes  of  typ.    It 
.in  be  found  that  the  larger  type  contains  a  course  P^cfcally  com- 
iLt  itself,  and  that  the  matter  of  the  smaller  type  is  chiefly  e^ 
plana^ry  of  the  former.    It  is  highly  desirable,  however,  that  U^ 
Cks^Ld  he  rea.  as  a  whole,  while  the  -tual  class^wo'k  may  be 
confined  to  the  subjects  treated  in  the  larger  type    '«  ^^«  ^J^*  " 
pressed  for  time.    A  celestial  globe,  and  a  set  of  B^«-^;;''  f  ""^^ 
L's  "  New  Star-Atlas"  is  as  good  as  any),  will  be  ^o^^^  t°  b«  °' 
L  in  connection  with  the  study ;  and  if  the  class  has  access  to  a  sm^l 
LTescope.  even,  much  can  be  learned  in  this  way.     ^  ™-    «^- 
glass  wUl  suffice  to  give  a  correct  notion  of  the  genera   features  of 
fhe  moon's  surface,  and  a  very  small  telescope,  if  properly  used,  will 
do  the  same  for  the  larger  planets. 


f 


~,.iaaii5a£p2iass- ':'':■ 


"^'IwtSS&B^MIHMML^ 


CONTENTS. 

PABT  I. 

INTRODUCTION. 


PAOB 


and  Abbreviations 

CHAPTER  I. 

,1  njmfln»lonB— The  Celestial  8pbere-Tbe 

Tl.e  Eartb's  Shape  and  Dlmen'S-Diunial  Motion  in  Different 

Horizon-The  D'"™"^**"^!'""  the  Terrestrial  and  Celestial 
Latitudes-Correspondence  of  the  lerresw ^^ 

Spheres 

CHAPTER  n. 
««r  Ti-ARTH  TO  Tffls  HKAVBi»-(Cbn«inu«D. 

RBIjATIOH  or  THK  KAUTH  T"   »•»" 

lr«t3rminatlon  of  Latltade^-P»«»>«-  • 

CHAPTER  HI- 
AOTROSomcAL  IsmBtmmrni. 
„  ^«—  .tia  mocks— The  Transit  Instm- 

—The  Nautical  Almanac 


COXTKNTS. 

CHAPTER  IV. 
MonoNB  OK  TiiK  Earth. 


PAOI 


Ancient  Ideaa  of  tlio  Ploncts— Anniml  Kcvoliition  of  the  Earth 
—The  Sun's  Apparent  Pulh— Obliqnily  of  tbo  Ecliptic— 
The  Seasons— Celestial  Latitude  and  Longitude gi 

CHAPTER  V. 
Tub  Planetary  Motions. 
Apparent  and  Real  Motions  of  the  Planets— The  Copcrnlcan 
System  of  the  World— Kepler's  Laws  of  Planetary  Motion . .    96 


CHAPTER  VL 

Universal  Oravitatioit. 

Newton's  Laws  of  Motion— Gravitation  in  tlie  Heiivcns— Mutual 
Action  of  the  Planets-  Remarks  on  the  Theory  of  Oravi- 
tation 


118 


CHAPTER  VH. 
The  Motions  and  Attraction  of  the  Moon. 
The  Moon's  Motions  and  Phases— The  Tides— Effect  of  the 
Tides  upon  the  Eartli's  Rotation 123 


CHAPTER  VIIL 

Eclipses  of  the  Sun  and  Moon. 

The  Earth's  Shadow-Eclipses  of  the  Moon-Ecllpscs  of  the 
Sun— The  Recurrence  of  Eclipses 


129 


CHAPTER  IX. 
The  Earth. 
Mass  and  Density  of  the  Earth- Laws  of  Terrestrial  Gnivitation— 
Figure  and  Magnitude  of  the  Earth— Geodetic  Surveys- 
Motions  of  the  Earth's  Axis,  or  Precession  of  the  Equinoxes 
—Sidereal  and  Equinocthil  Year— The  Causes  of  Precession  143 


tl  ..- 


tlie  Earth 
Ecliptic— 


PAom 


81 


npcrnican 
Motion.. 


90 


—Mutual 
of  Qravi- 


118 


ON. 

t  of  the 


123 


)  of  the 


129 


tation — 
irveys — 
|Uinoxc8 
ecession  143 


COMHNrS. 

CHAPTER  X. 
Cblkbtiai.  Mbabubbme«t»  or  Ma«  and  Distance. 


▼tt 


rAOS 


m.-  n«l,.«ilal  Scale  of  MeaBurcment-Mcasurcs  of  the  Solar  and 
^'^  S„«  irX-Mcthod.  of  Determining  the  Solar  Parallax 
-Relative  Masses  of  the  Sun  and  PlaneU »«» 

CHAPTER  XI. 

The  Refbaction  and  Abbrbation  of  Light  ;  Twilight. 
A.™o«nherlc  Rcfractlon-Qunntlty  and  Effects  of  Refractlon- 
""'Twlllit-A^ratlon  and  the  Motion  of  Llght-Dl««,very  ^^ 

and  EffecU  of  Aberration 

CHAPTER  XII. 

CUBONOLOGT. 

.Ions  of  the  Day-Equation  of  Time 


PART  II. 

THE  SOLAR  SYSTEM  IN  DETAIL. 

CHAPTER  I. 

&rRCCTlTBB  or  THE  SOLAB  STBTBM. 

Planets-Asterolds-Comets-Planetary  Aspects-Tables  of  th.  ^^ 
Elements  of  the  Solar  System 

CHAPTER  II. 
The  Sun. 
1  a..mn.arv-The  Photosphere-Light  and  Heat  from 
°*"t  S^^  JSTmount  0?  Heat  EmmedJ^^e  Sun- 
^lar  Temperature-SunSpots  and   ^"cu'*--?^  .^^ 
«d  Ba.»to%ature  of  Sun-Spots-Number  and  Periodic 
Uv  oisSar  8pot»-The  Sun's  Chromosphere  and  Corona 
-VaL^^Nat^reof  the  Prominen«*-The  Coron.^  Spec- 
truTsource.  of  the  Sun's  Heat-Theone.  of  th.  Sun.  ^ 
Constitution 


Vlii  COtiTKNTS. 

CHAPTKU  MI. 

Thk  InPKHIDH   Pl.AIIRTg. 

Motions  and  A«pecl8-Atni«H,,hero  nnU  Rotation  of  Merr.irv-"*" 
Atmosphcro  uiul  lU.Utlon  of  Vemis-TrunHlts  of  Mercury 
and  Vcuug-8u|ip<)8cd  Intrttmerciirlal  PlaneU 321 

CHAPTER  IV. 

TlIK  Mo<»N, 

Character  of  the  M^n's  Surface- Lunar  Almoapherc-Light 
and  Heat  of  the  Moou-Ia  tlicrc  any  Change  on  the  Surface 
oftheMooD? 

CHAPTER  V. 
The  Pi,ankt  Mars. 
DeBcrlplion  of  the  Planet -Rotation- Surface -Sntelliles  of 
**"" 233 

CHAPTER  VI. 
Tub  Minor  Planets 

The  Number  of  Small  Planets-Thelr  Magnitudes-Forms  of 
their  Orbits— Origin -«. 

CHAPTER  VII. 

Jupiter  and  nis  Satellitbb. 

The  Planet  Jupiter-Satellites  of  Jupiter 240 

CHAPTER  VIII 

Saturn  and  rib  Stbtbv. 

Oener.1  Descrlption-The  Rings  of  Saturn-Satellites  of  Saturn  240 

CHAPTER  IX. 

Thb  Planet  IJRANua 

Discotery— Si»»flllitc8 ^^ 


■mximmi 


Wercury— 
r  Mercury 


aai 


re— Light 
u  Surface 


•••••• I 


elliles  of 


233 


'orms  of 


240 


f  Saturn  246 


858 


vom'KNra.  *■ 

CIUPTBU  X. 

TlIK  Pl-ANBT  NKPTUNE.  ,aM 

,....„„...,U.„......nU.«.M.n„-D,„.v.r,_.uB.«>U..». 

CHAPTEU  XI. 
The  Phtmcm.  Co«otitution  of  the  Planets 

.  v,.nns-'rhc  Eurlli  and  MarB-Jupiltr  uiul  Salun. 

Mercury  mi"  Vcnu»—  •  n^  ^"  201 

— UVanui  and  Ncplune 

CHAPTER  XII. 
Meteors. 

CHAPTER  XIII. 

COMBTB. 

The  BesUUng  Medium 

PART  III. 

286 

INTRODUCTION 

CHAPTER  I. 

COHBTEI.1.ATIOSB. 

UieBtar*.... " 

CHAPTER  II. 

Variable  and  Tempobabt  Stabb. 

gtarsIteguMy  Varlnble-Temporary  or  New  8uts ^ 


r««i,T^,„r.,,,.  .n.»KL^!,!^a{iJUlMdKi 


nM«««iyM<  MNi  iH  wnuriii 


RBHBHHHHfckt 


X  CONTENTS 

CHAPTER  in. 
Multiple  Stars. 

PAOB 

Character  of  Double  and  Multiple  Stars— Binary  Systems 801 

CHAPTER  IV. 

NBBULiG  AND  CLUSTERS 

Discovery  of  Nebulae— Classiftcntion  of  Nebulae— Clusters— Star 
Clusters— Spectra  of  Nebulae,  Clusters,  and  Fixed  Stars— 
Motion  of  Stars  in  the  Line  of  Sight 804 

CHAPTER  V. 

Motions  and  Distances  op  the  Stars. 

Proper  Motions— Proper  Motion  of  the  Sun— Distances  of  the 
Fixed  Stars 313 

CHAPTER  VI. 

Construction  op  the  Heavens 

Star-gauging- The  Milky  Way 818 

CHAPTER  VII. 

CoSMOaONT. 

Laplace's  Nebular  HypoihcsiH— Oeneral  Conclusions 828 

INDEX aaa 


PAOB 

ms 801 


ASTRONOMY. 


ere— Star 
]  Stars— 


804 


;s  of  the 


813 


818 


INTRODUCTION. 


Artronomy  Deflnei-Astronomy  {a<frr,p-a  stei-,  and 
vo>"  a  llw)  is  the  science  which  has  to  do  with  he 
Lavenly  bodies,  their  ar>l>earanceB,  their  natur.,  and  the 
laws  governing  their  real  and  their  apparent  motions 

Tn'woaching  the  study  of  this  the  oldest  of  th. 
sciences 'depending  upon  observation,  it  must  be  homo  m 
n,iad  that  its  progress  is  most  intimately  <>onn^^  ^^^ 
It  of  the  race,  it  having  always  been  the  basis  of  ge<^- 
raphy  and  navigation,  and  the  soul  of  chronology.    Some 
71  chief  advances  and  discoveries  in  ab^ract  -the. 
„,atics  have  been  made  in  its  serv.oe,  and  the  method 
both  of  observation  and  analysis  once  peculiar  to  its  prac- 
Uce  now  furnish  the  firm  bases  upon  which  rest  that  great 
group  of  exact  sciences  which  we  call  Physics. 
^  It  is  more  important  to  the  student  that  he  should  be- 
come penetrated  with  the  spirit  of  the  methods  of  .^tron- 
omy  tlan  that  he  should  recollect  its  minut.«  ;  and  it   s 
most  important  that  the  knowledge  which  he  ""^y  «^° 
from  this  or  other  books  should  bo  referred  by  him  to  ite 
true  sources.    For  example,  it  will  often  be  necessary  to 
sSTf  certain  planes  or  circles,  the  ecliptic,  the  equa- 
tTtbe  meridian!  etc..  and  of  the  relation  of  the  appa- 


ABTRONOMT. 


rent  positions  of  stars  and  planets  to  them;  but  his  labor 
will  be  useless  if  it  has  not  succeeded  in  giving  him  a  pre- 
cise notion  of  these  circles  and  planes  as  they  exist  in  the 
sky,  and  not  merely  in  the  figures  of  his  text-book.  Above 
all,  the  study  of  this  science,  in  which  not  a  single  step 
could  have  been  taken  without  careful  and  painstaking 
observation  of  the  heavens,  should  lead  its  student  himself 
to  attentively  regard  the  phenomena  daily  and  hourly  pre- 
■ented  to  him  by  vhe  heavens. 

Does  the  sun  set  daily  in  the  same  point  of  the  horizon? 
Does  a  change  of  his  own  station  affect  this  and  <4her 
aspects  of  the  sky?  At  what  time  doe«  the  fuU  moon  rii»? 
Which  way  are  the  horns  of  the  young  moon  pointed? 
These  and  a  thonsand  other  questions  are  «lroM|y  vaamvnA 
by  the  obsarvant  eyes  of  the  ancients,  who  disooverad  not 
only  the  existence,  but  the  motion*,  of  the  vari<»i  plna»t^ 
and  gave  special  names  to  no  less  than  lonrscoie  ^an. 
The  modem  pupil  is  more  richly  eqaipped  fwr  observation 
than  the  ancient  philoaopher.  |f  one  oonW  hav»  pnt  % 
mere  opera.gUw8  in  the  hands  of  HiPVABoaire  the  world 
need  not  have  waited  two  thonsand  years  to  know  the 
natnra  of  that  early  mystery,  the  Milky  Way.  nor  wonW  it 
have  required  a  Oaliwo  to  discover  the  phases  of  Fmmm 
and  the  spots  on  the  sun. 

Astronomy  furnishes  the  principles  and  the  methods  by 
monna  ol  which  thousands  of  ships  are  navigated  vith 
lafety  and  oertainiy  from  port  to  port;  Iff  wWA  thn 
dimenaiona  of  the  earth  itself  are  fixed  with  higH  praoinoB} 
by  which  the  distances  of  the  sun,  the  pknetf,  and  the 
hri(^ter  stare  are  measured  nnd  detemined.  The  letaila 
of  these  methods  cannot  he  given  in  iA  eWmwIniy  wofk ; 
hnt  the  genrnd  prinoiplea  and  even  the  apiritol  tk« 


)at  his  labor 
I  him  a  pre' 

exist  in  the 
ook.  Above 
a  single  step 

painstaking 
ident  himself 
I  hourly  pre- 

the  horizon? 
lis  and  <^her 
til  moon  rise? 
>on  pointedf 
acljaniiraiied 
isooTerad  not 
ri<HU  phuirti^ 
nrscore  ^ank 
t  obserratioa 
i  hay9  p»t  « 
us  the  iForU 
to  know  the 

nor  woiUicI  it 
»aei  of  Fmmm 

«  methods  by 
iTigated  viA' 
^jr  whleh  ih* 
ughpieoiiuHi} 
aetf,  and  the 
,    The  letaik 

«WlfHIJWOfki 


INTRODUCTION. 


8 


methods  can  be  entirely  mastered  by  the  faithful  student. 
All  the  attention  which  he  can  bring  will  be  richly  reward- 
ed  by  the  insight  he  will  gain  into  the  noblest  of  the  physi- 
cal sciences.  .     .  , 

How  to  Study  Astronomy.-There  are  a  few  prmciples 
of  Mathematics,  of  Geography,  of  Physics,  which  must  be 
clearly  understood  by  the  student  commencing  astronomy, 
so  that  he  may  go  on  with  advantage.    They  are  all  quite 
simple,  but  they  must  be  entirely  fixed  in  the  mind,  in 
order  that  the  attention  may  be  directed  to  the  aatrommtcal 
principle  and  not  diverted  by  an  attempt  to  recollect  a  fact 
from  another  science.    Any  patience  and  concentration 
which  the  student  may  bestow  upon  them  at  the  outset 
should  be  rewarded  by  the  facility  with  which  they  will 
enable  him  to  grasp  the  more  interesting  portions  of  the 
subject.    The  few  definitions  which  are  given  ^^  ^^^^ 
should  be  memorized  in  the  words  of  the  text.     In  all  other 
cases  it  is  preferable  that  the  student  .uould  give  his  own 
explanations  in  his  own  words. 

First  we  will  go  briefiy  over  some  of  the  essential  mathe- 
matioal  principles  alluded  to.  , 

AiiKles:  their  lIeaMrement--^»  angU  is  the  amoufit 
of  divergence  of  two  right  lines.    For  example,  the  angle 
between  the  two  right  lines  S'E  and 
S*E  is  the  amount  of  divergence  of 
these  Unes.    The  angle  S'ES'  is  the 
amount  of  divergence  of  the  two  lines 
S'E  and  8*E.    The  eye  sees  at  once 
that  the  angle  8*E8*  in  the  figure  ia 
greater   than  the  angle  S'ES\  and 
that  the  angle  8*E^*  w  V^^^  ^^^ 
either  of  them. 


Wmi. 


niiiM  rii-  imm-m 


4  ASTRONOMT. 

In  order  to  compare  them  and  to  obtain  their  numerical 
ratio,  ve  must  have  a  unit-angle. 

The  unit  angle  is  obtained  in  this  way:  The  circumfer- 
ence of  any  circle  is  divided  into  360  equal  parts.  The 
points  of  division  are  joined  with  the  centre.  The  angles 
between  any  two  adjacent  radii  are  called  degrees.  In  the 
figure,  S'ES'  is  about  12°,  S'ES'  is  about  22°,  S^ES*  is 
about  30°,  and  S'ES*  is  about  64°.  The  vertex  of  the 
angle  is  at  the  centre  E:  the  measure  of  the  angle  is  on 
the  circumference  S'S'S*S\  or  on  any  other  circumference 
drawn  from  E  aa  a  centre. 

In  this  way  we  have  come  to  speak  of  the  length  of  one 
three-hundred-and-sixtieth  part  of  any  circumference  as  a 
degree,  because  radii  drawn  from  the  ends  of  this  part 
make  an  angle  of  1°. 

For  convenience  in  expressing  the  ratios  of  different 
angles  we  have  subdivided  the  degree  into  minntei  and 
seconds.  The  degree  is  too  large  a  unit  for  some  of  the 
purposes  of  astronomy,  just  as  the  metre  is  too  large  a  unit 
for  use  in  the  machine-shop,  where  fine  work  is  ooncemecL 


One  circumference  =  860°  =  21600'  =  1296000* 
r  =    60*  =860' 
1'  =    60' 

When  we  wish  to  express  smaller  angles  than  seconds, 
we  use  decimals  of  a  second.    Thns  one-qnarter  of  a  second 
,,  is  0'.26;  one  quarter  of  a  minnte  is  15'. 

'.  The  Radini  of  the  Cirde  in  Angular  ][eaiiix«i.--If  B  is 
:t)ie  radius  of  a  circle,  we  know  from  geometry  that  1  cir" 
^^^ifilwiferen^  —  2  7rR,  where  tc  =  3. 1416.    That  is. 


or 


2jtB=  860'  r=  21600'  =  1296000* 
fi  =  57".8  =  8437.7  =  206264'.R 


k  numerical 

circumfer- 
)arts.  The 
Tlie  angles 
es.  In  the 
°,  S'ES*  is 
rtex  of  the 
angle  is  on 
cumference 

igth  of  one 
erence  as  a 
f  this  part 

}f  different 
linntei  and 
lome  of  the 
large  a  unit 
I  concerned. 

00* 


tan  seconds, 
r  of  a  second 

xt^^If  S  is 
f  that  1  oir- 
latis. 


INTRODUOTION.  O 

By  this  we  mean  that  if  a  flexible  cord  equal  in  length 
to  the  radius  of  any  circle  were  laid  round  the  circumfer- 
ence of  that  circle,  and  if  two  radii  were  then  drawn  to  the 
ends  of  this  cord,  the  angle  of  these  radii  would  be  67°.  3, 
3437'.7,  or  206264'.  8. 

It  is  important  that  this  should  be  perfectly  clear  to  the 

student. 

For  instance,  how  far  off  must  you  phice  a  foot-rule  in 
order  that  it  may  subtend  an  angle  of  1°  at  your  eye? 
Why,  57.3  foet  away.  How  far  must  it  be  in  order  to  sub- 
tend an  angle  of  a  minute  ?  3437.7  feet.  How  far  for  a 
second  ?    206264.8  feet,  or  over  39  miles. 

Again,  if  an  object  subtends  an  angle  of  1°  at  the  eye, 

we  know  that  its  diameter  must  bo  ^^73  as  groat  m  its  dis- 
tance from  us!  If  it  subtends  an  angle  of  1',  iU  distance 
from  us  is  over  200,000  times  as  great  as  its  diameter. 

The  instruments  employed  in  astronomy  may  bo  used  to 
measure  the  angles  subtended  at  the  eye  by  the  diameters  of 
the  heavenly  bod  ies.  In  other  ways  we  determine  their  dis- 
tance from  ns  in  miles.  A  combination  of  these  data  will 
give  ns  the  actual  dimensions  of  these  bodies  in  miles. 
For  example,  the  sun  is  about  93,000,000  miles  from  the 
earth.  The  angle  snbtended  by  the  sun's  diameter  at  this 
distance  is  1922'.   What  is  the  diameter  of  the  sun  in  miles  ? 

An  idea  of  angular  dimensions  in  the  sky  may  be  had  by 
remembering  that  the  angular  diameters  of  the  moon  and 
of  the  sun  are  about  30'.  It  is  180°  from  the  west  point  to 
the  east  point  counting  through  the  point  immediately 
ovwfaead.  How  many  moons  placed  edge  to  edge  would  it 
take  to  reach  from  horizon  to  horiion  ?  The  student  may 
gneM  at  the  answer  first  and  then  compute  it 


BWiiSaitiiWiiiiiaiMMiMiliw 


0  ASTRONOMY, 

Perhapfl  a  more  convenient  measure  is  the  apparent  dis- 
tance apart  of  the  "  pointers"  in  the  Great  Dipper,  which 
is  6°.    (See  Fig.  7,  page  21.) 

Plane  Triangles.— The  angles  of  which  wo  have  hecn 
speaking  arc  angles  in  a  plane.  In  any  plane  triangle  there 
are  three  sides  and  three  angles— six  parts.  If  any  three  of 
these  parts  (except  the  three  angles)  are  given  we  can 
construct  the  triangle.  If  the  three  angles  alone  are  given 
we  can  make  a  triangle  which  shall  be  of  the  right  shape, 
and  that  is  all. 


Fio.  a. 


Splwrioal  Triangles —Besides  plane  angles  and  triangles, 
wo  have  to  do  with  those  drawn  on  the  surface  of  a  sphere 
-^spherical  triangles.  This  is  necessary  since  the  heavenly 
bodies  are  spherical  in  shape,  and  since  they  are  seen  pro- 
jected against  the 'concave  surface  of  the  sky. 

The  Sphere:  its  Planes  and  Circles.— In  the  figure,  0  is 
the  centre  of  the  sphere  and  ABE  is  one  of  its  circles. 
Suppose  a  plane  AB  passing  through  the  centra  and  oat- 


arent  dis- 
er,  which 

lave  been 
ngle  there 
y  three  of 
1  we  can 
are  given 
;ht  shape. 


1  triangles, 
if  a  sphere 
e  heavenly 
B  seen  pro- 

Sgure,  OU 
its  circles. 
«  and  cat- 


INTRODUCTION.  7 

ting  the  sphere  into  two  hemispheres.  It  will  intersect  the 
surface  of  the  sphere  in  a  circle  AEBFyf\^\c\x  is  called  a 
great  circle  of  the  sphere.  A  great  circle  of  the  sphere  w 
one  cut  from  the  surface  by  a  plane  passing  through  the 
centre  of  the  sphere.  Suppose  a  right  line  POP'  perpen- 
dicular to  this  plane.  The  points  P  and  P'  in  which  it 
intersects  the  surface  of  the  sphere  are  everywhere  90 
from  the  circle  AEBF.  They  are  the  poles  of  that  circle. 
The  poles  of  the  great  circle  CEDF  aro  Q  and  C'. 
The  following  relations  exist  between  the  angles  made 

in  the  figure:  ,  .    ..     • 

I.  The  angle  POQ  between  the  poles  is  equal  to  the  in- 
clination of  the  planes  \o  each  other. 

II.  The  arc  BD  which  measures  the  greatest  distance 
between  the  two  circles  is  equal  to  the  arc  PQ  which 
measures  the  angle  POQ. 

IIL  The  points  E  and  F,  in  which  the  two  great  cir- 
cles intersect  each  other,  are  the  poles  of  the  great  circle 
PQACP'Q'BD  which  passes  through  the  poles  of  the  first 

circle. 

The  Spherical  Triangle.^In  the  last  figure  there  aro 
several  spherical  triangles,  as  EDB,  FAC,  ECP'Q'B,  etc. 
In  astronomy  we  need  consider  only  those  whose  side* 
are  formed  by  arcs  of  great  circles.  The  angles  of  the 
triangle  are  angles  between  two  arcs  of  great  circles;  or  what 
is  the  same  thing,  they  are  angles  between  the  two  planes 
which  cut  the  two  arcs  from  the  surface  of  the  sphere. 

In  spherical  triangles,  as  in  plane,  there  are  six  parts, 
three  angles  and  three  sides.  Having  any  three  parts  the 
other  three  can  be  constructed. 

The  sides  as  well  as  the  angles  of  spherical  triangles  are 
expressed  in  degrees,  minutes,  and  seconds.    If  the  student 


'Td 


■::l 


I 


li 


g  A8TR0N0MT. 

has  a  globe  before  him,  let  him  mark  on  it  the  triangle 
whose  angles  are 

A  128°  44'  45M, 
B   33°  11'  12'.0, 
G  18°  15' SIM, 
and  whose  sides  are  (a  is  opposite  to  ^,  5  to  ^,  c  to  C.) 
a  =  10°,     J  =  7°,     c  =  4°. 

Power  of  the  Eye  to  see  Small  Objeoti. — When  a  round 
object  subtends  an  angle  of  1'  (that  is,  when  it  is  about 
3437  of  its  own  diameters  away),  it  is  just  at  the  limit  of 
yisibility,  under  ordinary  cii-cumstanccs.  At  the  Transit  of 
Venu8  in  1874,  the  planet  Venus  was  between  the  earth 
and  the  sun,  and  appeared  as  a  small  black  spot,  just  visi- 
ble to  the  naked  eye,  projected  on  the  sun's  face.  It  was 
67'  in  diameter. 

If  two  such  discs  are  nearer  together  than  1'  13',  few 
eyes  can  distinguish  them  as  two  distinct  objects.  If  a 
body  is  long  and  narrow,  its  angular  dimensions  (width) 
may  be  reduced  to  10'  or  15'  before  it  is  indistingnishable 
to  the  eye.     For  example,  a  spider  line  hanging  in  the  nir. 

If  an  object  is  very  much  brighter  than  the  background 
on  which  it  is  seen,  there  is  no  limit  below  which  it  is  nec- 
essarily invisible.  Its  visibility  depends,  in  such  a  case, 
only  on  its  brightness.  It  is  probable  that  the  diameters 
of  the  brightest  stars  subtend  an  angle  no  greater  than 
O'.Ol. 

Latitude  and  Longitude  of  a  Place  on  the  Earth's  SuiliMe. 
Geography  teaches  us  that  the  earth  is  a  sphere.  Positions 
on  its  surface  are  defined  by  giving  their  latitude  and 
longitude.  According  to  geography,  th«  latituth  of  a  place 
on  the  earth's  surface  is  its  angular  distance  north  or  south 
of  the  equator. 


INTRObUClWy. 


9 


D  triangle 


ioC.) 

Q  a  round 
t  is  about 
e  limit  of 
Transit  of 
tbo  earth 
just  visi- 
e.    It  was 

'  12',  few 
ccts.  If  a 
as  (widtli) 
Qgnisliablo 
iu  the  nir. 
nckground 
li  it  is  ncc- 
ch  a  case, 
diameters 
eater  than 

I'iSniliMe. 
Positions 
itude  and 
)  of  a  place 
\h  or  south 


Tin  longitude  of  a  place  on  the  earth's  surface  is  its 
angular  distance  east  or  west  of  a  given  first  tnertdian. 

If  P  in  the  figure  is  the  north  pole  of  the  earth,  the 
latitude  of  the  point  B  is  60°  north;  of  2  it  is  30°  north; 
of  /  it  is  27°i  south.  All  places  having  the  same  latitude 
are  situated  on  the  same  parallel  of  latitude.  In  the  figure 
the  parallels  of  Utitude  are  represented  by  straight  lines. 

All  places  having  theiame  longitude  are  situated  on  the 


FM.aL 


same  meridian.    We  shaU  give  the  astronomical  definitions 
of  these  terms  further  on. 

It  is  found  convenient  in  astronomy  to  modify  the  geo- 
graphical definition  of  longitude.  In  geography  we  say 
that  Washington  is  77°  west  of  Greenwich,  and  that  Syd- 
ney (Australia)  is  161°  east  of  Greenwich.  For  astro- 
nomical pniposes  it  is  found  more  convenient  to  count  the 


10 


A8TR0N0MT. 


'\f 


longitade  of  a  place  from  the  flnt  meridian  (nitially 
Greenwioli)  always  towards  the  weit.  Thus  Sydney  is  209° 
west  of  Greenwich.    360° -151  "=209°. 

The  earth  turns  on  its  axis  once  in  24  hoars.  In  this 
time  a  point  on  its  sarface  moves  through  860  degrees,  or 
such  a  point  moves  at  the  rate  of  16°  per  hour.  860  divided 
hy  24  is  15. 

Hence  we  may  express  the  longitude  of  a  place  either  in 
time  or  arc.  Washington  is  6^  8"  west  of  Greenwich,  and 
Sydney  is  IS**  50"  west  of  Greenwich. 

It  is  also  indifferent  which  first  meridian  we  choose. 
We  may  refer  all  longitudes  to  Paris,  to  Berlin,  or  to  Wash- 
ington. Sydney  is  8"  48"  west  of  Washington,  and  Green- 
wich is  IS**  62">  west  of  Washington. 

In  the  figure,  suppose  Ftohe  west  of  the  first  meridian. 
All  the  phKses  on  the  straight  line  PQ  have  a  longitude  of 
15°  or  1  hour;  all  on  the  curve  Pi'^Q  have  a  longitude 
of  75°  or  6  hours;  and  so  on. 

The  difference  of  longitude  of  any  two  placee  on  the  earth 
it  the  angular  distance  between  the  terrestrial  tneridiane 
passing  through  the  two  places* 

Thus  Washington  is  77°  west  of  Greenwich,  and  Sydney 
is  209°  west  of  Greenwich.  Hence  Sydney  is  132°  west  of 
Washington,  and  this  in  the  difference  of  longitude  of  the 
two  places. 


4L 


1  (ainally 
ney  is  209° 

■s.  In  this 
degrees,  or 
)60  divided 

ue  either  in 
nwioh,  and 

we  choose. 
ortoWash- 
and  Oreen- 

t  meridian, 
ragitude  of 
k  longitude 

m  iht  earth 
meridiatu 

tnd  Sydney 
Si'  west  of 
tade  of  the 


SYMBOLS    AND    ABBREVIATIONS 


naMB  0»  THB  PLAimW,  wto. 


®  or 


Tlie  Sun. 
The  Moon. 
Mercury. 
Venus. 
The  Earth. 


6 

V 


Man. 

Jupiter. 
Saturn. 
Uranus. 
Neptune. 


The  asteroids  are  distinguished  by  a  circle  enclosing  a  number, 
which  number  Indicates  the  order  o(  dlscoTery,  or  by  their  names, 
or  by  both,  as  @)  ;  HeeaU, 


noiiB  or  TBa  kodiao. 


Spring 
■igns, 


(1.  T 
«  U.  « 
••  /a  n 


Aries. 
Taurus. 
'.  8.  n  Qemtni. 
(4.  O  Canoer. 
Summers  J    ft  Leo. 

•*«°*    (e.iBl  Virgo. 


(  1. 
Autumn  \   g 

signs.   J   j' 
Wlnter^^  ■ 


£k  Libra. 
HI  Scorplus. 
f  Saf^ttarius. 
^  Cnpricomus. 
a  Aquarius. 
H  Pisces. 


The  Greek  alphabet  Ishere  inserted  to  aid  those  who  are  not  already 
familiar  with  It  in  reading  the  parts  of  the  teit  in  which  ito  lettera 
occur: 


UttMS. 

A  a 
Bfi 

rr 

J  8 
E  e 
ZC 
Ht, 

e  » 0 
/« 

AX 


Kames. 

Alpha 

BeU 

Oamma 

Delta 

Epsilon 

Zeta 

Eta 

Theto 

Iota 

Kappa 

Lambda 

Mu 


LrttoiSL 

N  V 

Si 

Oo 
n  nit 

pp 

sat 

Tr 
T  V 
9  9» 
XX 

am 


Ka 

Na 

Xi 

Omleron 

PI 

Bho 

Sigma 

Tau 

Uprilon 

Phi 

Chi 

Psl 

Omega 


mmuM'* 


19 


ABTRONOMT. 


THE     METRIC    SYSTEM. 


The  metric  nyatem  of  wcightt  nnd  meniurea  being  employed  In 
thii  volume,  the  following  reliillon»  between  the  unlu  of  tliin  iiyitcm 
most  uited  and  thoee  of  our  ordinary  one  will  be  fountl  convenient  for 
reference : 

MKAaURKB  or  LRMOTH. 

1  kilometre  =  1000  metres        =    0-63187  mile. 
1  metre         =  tbe  unit  =  89 -870  inciiei. 

1  millimetre  =  xin  »'  »  met™  =   0-08987  incb. 

MBAtUBEa  or  WRIOBT. 

1  kilofnvmme  =  1000  grammea  =   2- 2049  pnunda- 
1  gramme        =  the  unit  =  10-482  grains. 


The  following  rough  approximations  may  be  memorised  *. 

The  kilometi«  U  a  little  more  than  ^,  of  a  mile,  but  less  than  |  of 
a  mile. 
The  mile  is  1 A  kilometres. 
The  kilogramme  is  2|  pounds. 
The  pound  is  less  than  iialf  a  kilogramme. 
One  metre  is  8-8  feet. 

One  metre  la  80 -4  inches.  ' 

'       1  .  .         ■' 


ii.i-!' 


-. '  V- 


i 


j^iA 


4  y\ 


Pinploycil  li. 
tf  tliiH  nyitctn 
unvenient  for 


ile. 
lea. 
ich. 


jnda. 

DS. 


led  -. 

lesR  than  |  of 


CHAPTER  I. 
THE  UBLATION  OF  THE  EAUTH  TO  THE  HBAVBNa 

THX  EAiTrfs  Sham  amd  Dimmoii. 

The  earth  ii  a  globe  whoM  dimeMions  are  gigantic 
when  compared  with  our  ordinary  and  daily  ideas  of  size. 

lt>  shape  is  nearly  a  sphere,  as  has  been  abuuduntly 
proved  by  the  accurate  geodetic  surveys  which  have  been 
made  by  various  nations. 

Of  its  size  we  may  get  a  rough  idea  by  remembering 
tliat  at  the  present  time  it  requires  about  three  months  to 
travel  completely  around  it. 

To  these  familiar  facts  we  may  add  two  propositions 
which  are  fundamental  in  astronomy. 

I  The  earth  w  compMely  isolated  in  space.  The  most 
obvious  proof  of  this  is  that  men  have  visited  nearly  every 
part  of  the  earth's  surface  without  finding  anything  to  the 

contrary.  .. 

II  The  earth  is  one  of  a  vast  number  of  globular  bodies, 
familiarly  known  as  stars  and  planets,  moving  according 
to  certain  laws  and  separated  by  distances  so  immense  that 
the  magnitudes  of  the  bodies  themselves  are  insignificant  tn 
comparison  to  these  distances.  The  first  conception  which 
the  student  of  astronomy  has  to  form  is  that  of  living  on 
the  surface  of  a  spherical  earth  which,  although  it  seems  of 
immenie  die  to  him,  is  really  but  a  point  in  comparison 


-.-,i:^mm!3»^'.m't'*'!*n^'«-y-  '■•■* 


ur 


:u';.i 


14 


ASTRONOMY. 


!i 


!"i 


If 


m 


with  the  distances  which  separate  him  from  the  stars  which 
he  nightly  sees  in  the  sky. 

The  Celestial  Sphebs. 

When  we  look  at  a  star  at  night  we  seem  to  see  it  set 
against  the  dark  surface  of  a  hollow  sphere  in  whose  centre 

we  are. 

All  the  stars  seem  to  be  at  the  same  distance  from  us. 
When  we  stop  to  consider,  we  see  that  it  is  quite  possible 
that  some  one  of  the  many  stars  visible  may  be  nearer 
than  some  other,  but  as  we  have  no  immediate  method 
of  knowing  which  of  two  stars  is  the  nearer,  we  are  driven 
to  speak  of  their  apparent  positions  just  as  if  they  were 
bright  points  studded  over  the  inner  surface  of  a  large 
hollow  globe,  and  all  at  the  same  distance  from  us.  The 
radius  of  this  globe  is  unknown.  We  do  not,  however, 
think  of  any  of  the  stars  as  beyond  the  surface  and 
shining  through  it.  We  therefore  suppose  the  radius  of 
the  sphere  to  be  equal  to  or  greater  than  the  distance  of 
the  remotest  star. 

Students  generally  fail  at  the  outset  to  realize  two  very 
important  facts  in  relation  to  the  celestial  sphere.  First, 
that  for  all  ''-e  purposes  of  our  present  knowledge  the 
relative  positions  of  the  stars  on  its  surface  do  not  vary. 
Maps  were  made  of  these  positions  centuries  ago  which  are 
as  correct  now  as  old  maps  of  portions  of  the  earth.  The 
motions  of  the  earth  present  different  portions  of  the  celes- 
tial sphere  to  our  observation  at  different  times,  and  one 
who  has  not  thought  at  all  of  the  subject  might  by  that 
fact  be  led  to  suppose  that  changes  are  taking  place  in  the 
relative  positions  of  the  stars  themselves.  Most  people, 
however,  know  that  they  can  find  the  same  groups  of  stars 


.  iss^'  :'''^#B-'■ 


le  stars  which 


to  see  it  set 
I  whose  centre 

ance  from  us. 
quite  possible 
lay  be  nearer 
idiate  method 
we  are  driven 
,  if  they  were 
ice  of  a  large 
rom  UB.  The 
not,  however, 
B  surface  and 
the  radius  of 
he  distance  of 

)alize  two  very 
jphere.  First, 
knowledge  the 
B  do  not  vary, 
ago  which  are 
le  earth.  The 
ns  of  the  celes- 
times,  and  one 
might  by  that 
Dg  place  in  the 
Most  people, 
gronps  of  stars 


RELATION  OF  THE  EAltTH  TO  THE  HEAVENS.  15 

-"constellations,"  as  they  are  called-in  different  direc 
tions  from  the  observer's  location  on  the  earth,  n.ght  after 
night;  the  difference  in  the  directions  being  due  to  he 
eartli's  motions.  Reflection  on  the  foregoing  will  help  he 
student  to  realize  the  second  imporUnt  fact  alluded  to  m  the 
besinning  of  this  paragraph-that  for  most  practical  pur- 
poses of  astronomy  the  earth  may  be  regarded  as  a  pomt 


Fia.  4. 


in  the  centre  of  a  hollow  globe  whose  inside  surfaw.  w 
spotted  over  with  the  stars,  that  hollow  globe  corresponding 
tothe  celestial  sphere.  In  fact  ingenious  instruments  to 
illnstrate  some  of  the  truths  of  astronomy  have  been  made 
of  Urge  globes  of  glass  or  other  transparent  substanoe., 
with  the  stars  painted  in  their  unvarying  positiont  on  the 


16 


ABTRONOMT. 


inside  surface,  and  the  earth  snspended  at  the  centre  by 
supports  rendered  as  nearly  invisible  as  possible. 

Suppose  an  observer  at  the  point  0  in  the  figure.  If  he 
sees  a  star  at  the  point  Q  it  is  clear  that  the  real  star  may 
be  anywhere  in  space  on  the  line  OQ,  as  at  q  for  example, 
and  still  appear  to  be  at  Q. 

Again,  stars  which  appear  to  be  at  the  points  P,  'V,  U, 
T,  S,  R,  may  in  fact  be  anywhere  on  the  lines  OP,  0  V, 
OU,  OT,OS,OR.  Thus,  if  there  were  three  stars  along 
the  line  0  T,  they  would  all  be  projected  at  the  point  T  of 
the  celestial  sphere,  and  would  api>ear  as  one  star. 

The  celestial  sphere  is  the  surf  me  upon  which  we  im- 
agine the  stars  to  be  projected. 

The  projection  of  a  body  upon  the  celestial  sphere  is  the 
point  in  which  this  body  appears  to  bo,  when  seen  from 
the  earth.  This  point  is  also  called  the  apparent  position 
of  the  body.  Thus  to  an  observer  at  0,  T  is  the  apparent 
position  of  any  of  the  stars  whose  true  positions  are  t,  t,  t. 
Hence  it  follows  that  positions  on  the  celestial  sphere  re- 
present the  directions  of  the  heavenly  bodies  from  the  ob- 
server, but  have  no  necessary  relation  to  their  distances. 

If  the  observer  changes  his  position,  the  apparent  posi- 
tions lof  the  stars  will  also  change. 

We  need  some  method  of  describing  the  apparent  posi- 
tions of  stars  oh  the  celestial  sphere;  to  do  this  we  im- 
jigine  a  number  of  great  circles  to  be  drawn  on  its  surface, 
and  to  these  circles  we  refer  the  apparent  positions  of  the 
stars. 

A  consideration  of  Fig.  2  will  show  the  correctness  of 
the  following  propositions,  which  it  is  necessary  should  be 
clearly  understood : 

L  Every  straight  line  through  the  observer,  when  pro- 


M 


the  centre  by 

>le. 

figure.    If  he 

real  star  may 

for  example, 

uts  P,  'V,  U, 

icaOP,  or, 

CO  stars  along 
he  point  T  of 
star. 
which  we  im- 

l  sphere  is  the 
en  seen  from 
Trent  position 
I  the  apparent 
ons  are  /,  /,  t. 
Hal  Hphere  re- 
from  the  oh' 
distances. 
ipparent  posi* 

apparent  posi- 
o  this  we  im- 
on  its  rarface, 
ositionB  of  the 

correctness  of 
sary  should  be 

rer,  when  pro- 


BELATION  OF  THE  EAJiTU  TO  THE  HEAVENS.  17 

duced  indefinitely,  intersects  the  celestial  sphere  in  two 
opposite  points. 

II.  Every  plane  through  the  observer  intersects  the 

sphere  in  a  great  circle. 

III.  For  every  such  plane  there  is  one  lino  through  the 
observer's  position  which  intersects  the  plane  at  light 
angles.  This  lino  meets  the  sphere  at  tho  poles  of  the 
gi-eat  circle  which  is  cut  from  the  sphere  by  the  plane. 

Example:  PP',Fig.  2,  is  a  line  through  0  perpendicular 
to  the  plane  ^  5.    P,  P' are  the  poles  of  ^ -R 

IV.  Every  line  through  the  centre  has  one  plane  perpen- 
dicular to  it,  which  plane  cuts  the  sphere  in  a  great  circle 
whose  poles  are  the  intersection  of  tho  line  with  the 

sphere.  t,  v  /i 

Example:  The  line  QQ'hfiBone  plane  ^i?  through  O 

perpendicular  to  it,  and  only  this  one. 

The  Hobi^. 

A  hvel  plane  touching  the  spherical  earth  at  the  point 
where  an  observer  stands  is  called  the  horizon  of  that 

This  plane  cnts  the  celestial  sphere  in  a  great  circle, 
which  is  called  the  celestial  horizon.  The  celestial  horizon 
is  therefore  the  boundary  between  the  visible  and  the  in- 
visible hemispheres  to  that  observer. 

The  Vertical  Line.— The  vertical  line  of  any  observer  w 
the  direction  of  a  plumb-line  where  he  stands.  This  line 
is  perpendicular  to  his  horizon.  It  intersects  the  celestnd 
sphere  in  two  points,  called  the  zenith  and  the  nadtr  of 

that  observer.  , .        j  •    i 

The  zenith  of  an  observer  is  the  point  where  hts  vertical 

line  cuts  the  celestiitl  sphere  abovf  Ms  Aw?. 


m  I 


18 


AarRONO^r. 


The  nadir  of  an  observer  is  the  point  where  his  vertical 
line  cuts  the  celestial  sphere  below  his  feet. 

The  zenith  and  nadir  are  the  poles  of  the  horizon. 

Vertical  Planei  and  Cirolei.— A  vertical  plane  with  re- 
spect to  any  observer  is  a  plane  which  contains  his  vertical 
line.  It  must  pass  through  his  zenith  and  nadir  and  must 
be  perpendicular  to  his  horizon. 

A  vertical  plane  cuts  the  celestial  sphere  in  a  verticai 

circle. 
As  soon  as  we  imagine  an  observer  to  be  at  any  point  on 

^  the  earth's  surface  his  horizon 
is  at  once  fixed;  his  zenith 
and  nadir  are  also  fixed.  From 
his  zenith  nidiate  a  number 
of  vertical  circles  which  cut  the 
celestial  horizon  perpendicu- 
larly, and  unile  again  at  his 
nadir.  This  is  a  system  of 
lines  and  circles  which  every 
person  carries  about  with 
him,  as  it  were,  and  which  may  eerve  him  for  lines  to 
which  to  refer  the  apparent  position  of  every  etar  which  he 


Some  one  of  these  vertical  circles  will  pass  through  any 
and  every  star  visible  to  this  observer. 

ri«  altitude  of  a  heavenly  body  is  its  eUvation  dbtm  the 
plane  of  the  horizon  measured  on  a  vertical  circle  through 

the  star. 

The  zenith  distance  of  a  star  is  its  angular  d%slancefrom 
the  zenith  measured  on  a  vertical  circle. 

In  the  figure,  ZS'w  the  zenith  distance  (5)  of  S,  and 
H8{a)  is  its  altitude.    ZSUiimto  of  »  great  oirde; 


■^s^igti00eisBSi 


^mmmMmtwNaiHtim 


.'.Itjit'^l' 


J 


his  vertical 

rizun. 

ine  with  re- 

his  vertical 

lir  and  must 

a  a  vertical 

my  point  on 
)  bis  horizon 
;  his  zenith 
fixed.  From 
e  a  number 
rhich  cut  tbo 
perpcudicu- 
again  at  his 
a  system  of 
which  every 
about  with 
1  for  lines  to 
star  which  he 

through  any 

tion  above  the 
circle  through 

dietaneefrom 

{Z)  of  8,  and 
k  great  oirdei 


BELATION  OF  TUB  EABTH  TO  THE  UEAVBN8.  19 

the  vertical  circle  through  the  star.    ZSH  =  a  +  Z  =  90°, 
and  5  =  90°  -  a  or  o  =  90°  -  Z. 

The  altitude  of  a  star  in  the  zenith  is  90°;  half  way  from 

the  zenith  to  the  horizon  it  is  45°;  in  the  horizon  it  is  0°. 

Theatimuth  of  a  star  is  tlte  angular  distance  from  the  point 

where  the  vertical  circle  through  it  meets  the  horizon,  to  the 

north  {or  south)  point  of  the  horizon. 

In  the  figure,  NHxn  the  azimuth  of  S.  The  azimuth 
of  a  star  in  the  east  or  west  is  90°. 

The  prime  vertical  of  an  observer  is  that  one  of  his  verti- 
cal circles  which  passes  through  his  east  and  west  points. 

Coordinates  of  a  8Ur.— The  apparent  position  of  a  heav- 
enly  body  is  completely  fixed  by  means  of  its  altitude  and 
azimuth.  If  we  know  the  altitude  and  azimuth  of  a  star 
we  can  point  to  it. 

If,  for  example,  its  azimuth  is  20'  from  north  towards 
the  west  and  if  its  altitude  is  30°,"  we  can  point  to  the  star  by 
measuring  an  angle  of  20°  from  the  north  point  towards 
the  west,  which  will  fix  the  foot  of  a  vertical  circle  through 
the  star.  The  star  itself  will  bo  on  the  vertical  circle,  30° 
above  the  horizon. 

This  point,  and  this  alone,  will  correspond  to  the  posi- 
tion of  the  star  as  determined  by  its  altitude  and  azimuth. 
Numbers  {or  quantities)  which  exactly  define  the  position 
of  a  body  are  called  its  co-ordinates. 

Hence  altitude  and  azimuth  form  a  pair  of  co-ordinates 
which  fix  the  apparout  position  of  a  star  on  the  celestial 

sphere. 

It  must  be  remembered  that  these  two  co-ordinates  give 
only  the  position  of  ihe  projection  of  the  star  on  the  celes- 
tial sphere,  and  give  no  knowledge  of  its  distance  from  the 
obserTor,    The  body  may  be  any  where  o*  thQ  Une  defined 


l|^!3iW9WB(IIB™M«BWiiBSpSS^B^^W 


MiHBUfi 


w 


^  ASTRONOMY. 

by  the  position  on  the  celestial  sphere  and  the  place  of  the 

If  we  also  know  the  distance  of  the  star  from  the  ohaer- 
ver,  we  know  every  possible  fact  as  to  its  place  in  space. 

Thus,  three  co-ordinates  suffice  to  fix  the  absolute  position 
of  a  body  in  space;  two  co-ordinates  suffice  to  determine  its 
apparent  position  on  the  celestial  sphere. 

These  propositions  suppose  the  place  of  the  observer  to 
be  fixed,  since  the  altitude  and  azimuth  refer  to  an  obser- 
ver  in  some  one  definite  position.  If  the  observer  should 
change  his  place,  the  star  remaining  fixed,  the  apparent 
position  of  the  star  on  the  celestial  sphere  would  change  to 
him  owing  to  his  own  motion.  The  numbers  which  ex- 
presi  this  apparent  position-the  altitude  and  azimuth  of 
the  star— would  also  change. 

But  wherever  the  observer  is,  if  he  has  these  two  co- 
ordinates for  a  star,  the  apparent  place  of  the  star  is  fixed 

for  him.  .    ,  .    .  J 

The  Horiioii.— Since  the  earth  is  spherical  m  form,  and 
the  horizon  is  a  plane  touching  this  sphere,  every  different 
place  must  have  a  different  horizon.  Wherever  an  observer 
goes  on  the  earth's  surface  he  carries  an  horizon,  a  zenith^ 
and  a  nadir  with  him,  and  a  set  of  vertical  circles  to  which 
he  can  refer  the  positions  of  all  the  stars  he  sees.    If  he 
stays  at  a  fixed  point  on  the  earth's  surface  his  horizon  is 
always  fixed  with  relation  to  his  vertical  line.    But  Oje 
earth  on  which  he  stands  is  turning  round  its  axis,  and  hw 
horizon  being  tangent  to  the  earth  is  moving  ako,  and  the 
vertical  line  moves  with  it    The  stars  stay  in  the  B«ne  abM- 
lute  places  from  year  to  year.    The  earth  on  which  ^ 
observer  stands  is  turning  round  from  west  to  east    His 
horiisonia  thus  brought  successively  to  the  east  of  the  varioug 


m 


>lace  of  the 

a  the  ohser- 
in  space. 
ute  position 
etermine  itt 

I  observer  to 
to  an  obser- 
»rver  should 
he  apparent 
Id  change  to 
irs  which  ex- 
l  azimuth  of 

bese  two  co- 
I  star  is  fixed 

in  form,  and 
rery  different 
r  an  obserrer 
on,  a  zenith, 
cles  to  which 
)  sees.    If  he 
lis  horizon  is 
ne.    But  the 
axis,  and  his 
also,  and  the 
he  seme  abio- 
on  which  the 
to  east    Hit 
;of  theT»rioa« 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.  21 

stars,  which  thus  appear  to  rise  higher  and  higher  above 

it. 

The  earth  continues  its  motion,  and  the  plane  of  his  ho- 
rizon finally  approaches  the  same  stars  from  the  west  and 
they  set  below  it,  only  to  repeat  this  phenomenon  with 
every  rotation  of  the  earth. 

The  horizon  appears  to  each  observer  to  be  the  stable 
thing,  and  the  motion  is  referred  to  the  stars.  As  a  matter 
of  fact  it  is  the  stars  that  stand  still  and  the  horizon  which 
moves  below  them,  causing  them  to  appear  to  rise,  and  then 
above  them,  causing  them  to  appear  to  set. 

tmt  DiDBVix  Mono*. 

The  diurnal  motion  is  that  apparent  motion  of  the  sun,  . 
moon,  and  stars  from  east  to  west  in  consequence  of  which 
they  rise  and  set. 

We  call  it  the  diurnal  motion  because  it  repeats  itself 
from  day  to  day.  The  diurnal  motion  is  caused  by  a  daily 
rotation  of  the  earth  on  an  axis  passing  through  its  centre 
called  the  axis  of  the  earth. 

This  axis  intersects  the  earth's  surface  in  two  opposite 
points  called  the  north  and  south  poles  of  the  earth.  If  the 
earth's  axis  be  prolonged  in  both  directions,  it  meets  the 
celestial  sphere  in  two  points  which  are  called  the  poles  of 
the  celestial  sphere  or  the  celestial  poles.  The  north  celes- 
tial pole  corresponds  to  the  north  end  of  the  earth's  axis; 
the  south  celestial  pole  to  the  south  end. 

The  plane  of  the  equa  )or  is  that  plane  which  passes 
through  the  earth's  centre  perpendicular  to  its  axis.  This 
phme  intersects  the  earth's  surface  in  a  great  circle  of  the 
earth's  sphere  which  is  called  the  earth's  equator  {eq  in 
Fig.  6). 


,  .-i:.."^4i'';i«*Hi^  j^;-..E."-IiS 


■a^ 


M^ 


m 


m 


g2  ASTltONOMY. 

This  piano  intersects  the  celestial  sphere  in  a  great  circle 
of  this  sphere  which  is  called  the  celestial  equator  or  equi- 
noctial (EQ  in  Fig.  C).  ,   *   --«  ^^^a 

The  celestial  equator  is  everywhere  half  way  between  the 
two  celestial  poles  and  thus  90''  from  each.  The  celestial 
poles  are  thus  the  poles  of  the  celestial  equator. 

Apparent  Diurnal  Motion  of  the  Celeitial  Bphere-The 


fl4.& 


Observer  on  the  earth  is  nnconsoious  of  its  rotation,  and 
the  celestial  sphere  appears  to  him  to  revolve  from  east  to 
west  around  the  earth,  while  the  earth  appears  to  remain 
at  rest.  The  case  is  much  the  same  as  if  he  was  on  a 
steamer  which  is  turning  round,  and  as  if  he  saw  the  bar- 
bor-shores,  the  ships,  and  the  houses  apparently  turning  m 
an  opposite  dirwtiofli 


great  circle 
lor  or  equi- 

letween  the 
'he  celestial 

(here.— The 


rotation,  and 
from  east  to 

an  to  remain 
he  was  on  a 

9  saw  the  har- 

tly  tnrning  in 


BBLATION  OF  TUB  EARTH  TO  TUB  UBAVEN8.  23 

So  far  as  appea.  ea  are  concerned,  it  is  (inite  the  same 
thing  whether  we  conceive  the  earth  to  be  at  rest  and  the 
heatens  to  turn  about  it,  or  whether  we  conceive  the  stars 
to  remain  at  rest  and  the  earth  to  move  on  its  axis.  We 
can  explain  all  the  phenomena  of  the  diurnal  motion  in 
either  way.  We  must,  however,  remember  that  it  really  is 
the  earth  which  turns  on  its  axis  and  successively  presents 
to  the  observer  different  parts  of  the  celestial  sphere.  The 
parts  to  his  east  are  just  coming  into  view  (rising  above  his 
horizon).  The  parts  to  his  west  are  about  to  disappear, 
(setting  below  his  horizon). 

Since  the  diurnal  motion  is  an  apparent  rotation  of  the 
celestial  sphere  about  a  fixed  axis,  it  follows  that  there 
must  be  two  points  of  this  sphere  that  remain  at  rest; 
namely,  the  two  celestial  poles.  Moreover,  since  the  celes- 
tial poles  are  opposite  points,  .one  pole  must  be  above  the 
horizon  and  therefore  a  visible  point  of  this  sphore,  and 
the  other  pole  must  be  below  the  horizon  and  therefore  in- 
visible. .     „  ,, 

The  celestial  pole  visible  to  observers  in  the  northern 
hemisphere  is  the  north  pole.  To  locate  its  place  in  the 
sky  let  the  student  look  at  the  northern  sky  on  any  dear 

evening.  .  ,  . 

He  will  see  the  stars  somewhat  as  they  are  represented  in 

the  figure.  ,        .„  . 

In  fact  Fig.  T.  shows  the  stars  as  they  will  appear  to 
an  observer  in  the  month  of  August  in  the  early  hours  of 
the  evening.  But  theconfigurations  of  the  stars  can  be 
recognized  at  any  other  time. 

The  first  star  to  be  identified  is  PoUria,  or  the  Pole  Star. 
It  may  be  found  by  means  of  the  Pointers,  two  stars  in  the 
constelUtion  Ursa  Major,  famiHarly  known  as  the  Great 


wmmiiHli.im^'t 


mmmm 


II 


94  AarsoNOMT. 

Dipper.  The  Btraight  line  throngli  these  Btors,  as  shown 
in  the  figure,  posses  near  Polaris.  Polaris  is  U  degrees 
from  the  true  pole.  There  is  no  star  exactly  at  the  pole 
itself. 

The  altitude  of  the  pole-star  above  the  horizon  of  any 
place  is  equal  to  the  latitude  of  the  place,  as  will  be  shown 


rm.  T. 

hereafter.  Hence  in  most  parts  of  the  United  States  the 
north  pole  is  from  30°  to  45°  above  the  horizon.  In  Eng- 
land it  is  61°,  in  Norway  80°. 

I%e  north-polar  distance  of  a  star  is  its  angular  distanet 
from  the  north  celestial  pole. 


kwsMb 


nSlATtOlr  OF  THK  SAltrH  To       /f  n/SAl'^m  9| 


as  shown 

i  degreei 

the  pole 

on  of  any 
be  shown 


States  the 
.    In  Eng- 

!0r  di»tanc» 


The  following  laws  of  the  diurM*!    aotioii  wil    now  be 

clear: 

I.  Every  »tar  in  th»  heavens  appears  to  describe  a  circle 
tttound  the  pole  as  a  centre  in  consequence  of  (he  diurnal 

motion. 

II.  The  greater  tin  star's  north-polar  distance  the  larger 

is  the  circle. 

III.  All  the  stars  describe  their  diurnal  orbits  in  the 
$ame  interval  of  time,  which  is  the  time  required  for  th$ 
earth  to  turn  once  on  its  axis. 

The  circle  which  a  star  appears  to  describe  in  the  sky  in 
consequence  of  the  diurnal  motion  of  the  earth  is  called  the 
diurnal  orbit  of  that  star. 

These  laws  can  be  proved  by  obsei-yation.  Tlw  student 
can  satisfy  himself  of  their  correctness  in  any  clear  i^ight. 

If  the  star's  north-polar  distance  is  less  than  the  altitude 
of  the  pole,  the  circle  which  the  star  describes  will  not 
meet  the  horizon  at  all,  and  the  star  will  therefore  neither 
rise  nor  set,  but  will  simply  perform  an  apparent  diurnal 
rcTolution  round  the  pole.  Such  stars  are  shown  in  the 
figure.  The  apparent  diurnal  motion  of  the  stars  ii  in  the 
direction  shown  by  the  arrows  in  the  cut.  Below  the 
pole  the  stars  appear  to  more  from  left  to  right,  west  to 
east ;  abore  the  pole  they  appear  to  moye  from  east  to 

west. 

The  circle  within  which  the  stars  neither  rise  nor  set  is 
called  the  eireU  of  perpetual  apparition.  The  radius  of 
this  circle  is  equal  to  the  altitude  of  the  i)ple  above  the 
iMrison,  or  to  the  north  pohir  distance  of  tihe  north  point 

of  the  horison.  ,.^ 

As  a  lesnlt  of  this  apparent  motion  each  ii\diTidnal  con- 
gtetfvtion  dumges  its  configuration  with  r^jgpect  to  the 


I 


mmittiiiSSiim 


91 


ABTRomMT. 


horizon.  That  part  of  the  comtellation  which  in  highett 
when  the  group  i«  above  the  pole  becomes  lowwt  when  it 
Is  below  the  pole.  This  i>  shown  in  the  figure,  which 
represents  a  supposed  constellatioa  at  diflercMt  times  of  the 
night  as  it  revolves  round  t\\e  pole.  The  culmination  of  a 
star  occurs  when  it  is  at  its  highest  point  above  the  hori- 
lon.  The  jwint  of  culmination  is  midway  between  the 
points  of  rising  and  setting. 
If  the  polar  distance  of  a  star  exceeds  the  altitude  of  the 


Fia.  a 


pole,  the  star  will  dip  below  the  horizon  for  a  i'Wt  of  its 
diurnal  orbit,  and  the  greater  the  polar  distance  of  the 
star  thd  longer  it  will  be  below  the  horizon. 

A  star  whose  polar  distance  is  90"  lies  on  the  celestial 
equators  and  one  half  of  its  diurnal  orbit  is  above  and 
one  half  below  the  horizon.  ' 

The  fan  is  in  the  celestial  equator  about  March  Slst  and 
September  21st  of  each  yoai,  ao  that  at  th^  times  the 


^Ama 


in  higheit 
at  when  it 
ire,  which 
mes  of  the 
nation  of  a 
9  the  hori- 
)tween  the 

bude  of  the 


I  ^>Art  of  its 
Bnce  of  the 

the  celeitial 
I  above  and 

rch  Slit  and 
e  timed  the 


RMLATWlf  OP  TUS  KAHTH  TO  THK  ttKAVBSB.  97 

dayi  and  night,  are  of  equal  length.    Thii  ii  why  the 
celortial  equator  waa  formerly  called  the  equinoctial. 

Looking  further  wuth  at  the  celestial  sphere,  we  ihall 
gee  Btani  which  rise  a  little  to  the  ea«t  of  the  south  point  of 
the  horizon  and  set  a  little  to  the  west  of  this  point,  being 
above  the  horizon  but  a  short  time.  The  south  pole  is  as 
far  below  the  horizon  of  any  place  as  the  north  pole  is  above 
it.  Hence  stars  near  the  south  pole  never  rise  in  uur 
latitudes.  The  circle  within  which  stars  never  nae  is  called 
the  circle  of  perpetual  occultation. 

It  is  clear  that  the  positions  of  the  circles  of  perpetual 
apparition  and  occultation  depend  upon  the  \  --tion  of  the 
observer  upon  the  earth,  and  hence  that  they  will  change 
their  positions  (is  the  obse»  fer  changes  his. 

By  going  to  Florida  we  may  see  groups  of  stars  which 
are  not  visible  in  the  latitude  of  New  York. 

The  Meridian.— The  pJane  of  the  meridian  of  an  observer 
is  that  otte  of  his  vertical  planes  which  contains  the  earth's 
»:-  >.  Being  a  vertical  plane  it  must  contain  the  senith 
an  nadir  of  the  observer;  as  it  contains  the  earth's  axis 
it  must  contain  the  north  and  s.>uth  celestial  poles. 

Different  observers  have  different  meridian  planes,  since 
they  have  different  zeniths. 

The  terrestrial  meridian  of  an  observer  is  the  line  in 
which  the  plane  of  his  meridian  intersects  the  surface  of 
the  earth.    It  is  his  north  and  south  line. 

It  follows  that  if  several  observers  are  due  north  and 
south  of  each  other,  they  have  the  same  terrestrial  meridian. 
The  celestial  meridian  of  an  obwsrver  is  the  great  circle 
cut  from  the  celestial  sphere  by  the  phme  of  that  observer's 
meridian.  Persons  on  the  same  terrestrial  meridian  have 
the  same  celestial  meridian. 


in 
11 


n 


\i) 


Sd 


AamoifbitT. 


Terrestrial  meridianB  are  considered  as  l)eloDgiog  to  thd 
places  through  which  they  pass.  For  example,  we  speak 
of  the  meridian  of  Greenwich  or  of  the  meridian  of  Wash- 
ington, and  hy  this  we  mean  the  (terrestrial  or  celestial) 
meridian  lines  cut  out  by  the  meridian  plane  of  the  Boyal 
Observatory  at  Greenwich  or  the  Naval  Observatory  at 
Washington. 

The  Diubval  Xotiom  ni  Jtawaaan  "LktamoM. 

As  we  have  seen,  the  celestial  horizon  of  an  observer  wiU 
change  its  place  on  the  celestial  sphere  as  the  observer  travels 


fks.  t.  TM  ^AmuUB. 


from  place  to  place  on  the  snrfiice  of  the  earth.  If  he 
moves  directly  toward  the  north  his  zenith  will  approach  the 
north  pole;  but  as  the  zenith  is  not  a  visible  point,  the 
motion  will  be  naturally  attributed  to  the  pde,  which  will 
seem  to  approach  the  point  overhead.  The  new  apparent 
position  of  the  pole  will  change  the  aspect  of  the  obBenfer'fl 
sky,  as  the  higher  the  pole  appears  above  the  horiion  tli9 


teloDgiog  to  thd 
hmple,  we  spealc 
ridian  of  Wash- 
ial  or  celestial) 
ne  of  the  Boyal 
Obserratory  at 


LlTITUSIli 

m  obseryer  will 
observer  travelB 


9  earth.  If  he 
ill  approach  the 
iiUe  point,  the 
)de,  which  will 
)  new  apparent 
f  the  obBenier'fl 
ihe  horiion  the 


nJSLATJ02f  Of  THU  HABTlt  TO  TllS  HEAVENS.  29 

greater  the  circle  of  perpetual  apparition,  and  therefore  the 
greater  the  number  of  stars  which  never  set. 

If  the  observer  is  at  the  north  pole  his  zenith  and  the 
pole  itself  will  coincide  :  half  of  the  stars  only  will  be  vis- 
ible,  and  these  will  never  rise  or  set,  but  appear  to  move 
around  in  circles  parallel  to  the  horizon.  The  hori-^on  and 
the  celestial  equator  will  coincide.  The  meridian  will  be 
indeterminate  since  Zand  P  coincide;  there  will  be  no  east 
and  west  line,  and  no  direction  but  south.  The  sphere  in 
this  case  is  called  a  parallel  sphere,    (See  Fig.  9.) 


Vm.  M.— TnBraar 


If  instead  of  travelling  to  the  north  the  observer  should 
go  toward  the  equator,  the  north  pole  would  seem  to  ap- 
proach his  horison.  When  he  reached  the  equator  both 
poles  wottld  be  in  the  horizon,  one  north  and  the  other 
Mmtfa.  All  the  stars  in  succession  would  then  be  visible, 
and  W5h  would  be  an  equal  time  above  and  below  the 
horiaon.    (See  Fig.  10.) 

The  sphere  in  this  case  is  called  a  right  sphere,  because 
the  diurnal  motion  is  at  right  angles  to  the  horizon.    If 


MMM 


IH, 


80 


ASTRONOMY. 


now  the  observer  travels  southward  from  the  equator,  the 
south  pole  will  become  elevated  above  his  horizon,  and  in 
the  southern  hemisphere  appearances  will  be  reproduced 
which  we  have  already  described  for  the  northern,  except 
that  the  direction  of  the  motion  will,  in  one  respect,  be 
different.  The  heavenly  bodies  will  still  rise  in  the  east 
and  set  in  the  west,  but  those  near  the  equator  will  pass 
north  of  the  zenith  instead  of  south  of  it,  as  in  our  lati- 
tudes. The  sun,  instead  of  moving  from  left  to  right, 
there  moves  from  right  to  left.  The  bounding  line  be- 
tween the  two  directions  of  motion  is  the  equator,  where 
the  sun  culminates  north  of  the  zenith  from  March  till 
September,  and  south  of  it  from  September  till  March. 

If  the  observer  travels  west  or  east  of  his  first  station, 
his  zenith  will  still  remain  at  the  same  angular  distance 
from  the  north  pole  as  before,  and  as  the  phenomena 
caused  by  the  earth's  diurnal  motion  at  any  place  depend 
only  upon  the  altitude  of  the  elevated  pole  at  that  place, 
these  will  not  be  changed  except  as  to  the  times  of  their 
occurrence.    A  star  which  appears  to  pass  through  the 
zenith  of  his  first  station  will  also  appear  to  pass  through 
the  zenith  of  the  second  (since  each  star  remains  at  a  con- 
stant angnhir  distance  from  the  pole),  but  hit«r  ia  time, 
since  it  has  to  pass  through  the  zenith  of  every  place  be- 
tween the  two  stations.    The  horizons  of  the  two  stations 
will  intercept  different  portions  of  the  celestial  sphere  at 
any  one  instant,  but  the  earth's  rotation  will  present  the 
same  portions  successively,  and  in  the  same  order,  at  both. 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.  31 


e  equator,  the 
irizon,  and  in 
w  reproduced 
rthern,  except 
ne  respect,  be 
se  in  the  east 
lator  will  pass 
M  in  ourlati- 
left  to  right, 
nding  line  be- 
jqnator,  where 
[)m  March  till 
bill  March. 
B  first  station, 
gular  distance 
lie  phenomena 
f  place  depend 
)  at  that  place, 
times  of  their 
8  through  the 
0  pass  through 
mains  at  a  con- 
later  in  time, 
every  place  be- 
M  two  stations 
wtial  sphere  at 
rill  present  the 
order,  at  both. 


COBBlffOKDlirCB  OF  THE  TMBMTEIAI  AOT  CBIMTUI 

8FHEBE8. 

We  have  seen  that  the  altitude  of  the  pole  above  the 
horizon  of  any  observer  changes  as  the  observer  changes 
his  place  on  the  earth's  surface.  The  exact  relation  of  the 
altitude  of  the  pole  and  the  horizon  of  any  ob^rver  ,B 
expressed  in  the  following  Theorem:  The  altitude  of  m 
celestial  pole  above  the  horizon  of  any  place  on  the  earth  s 
surface  is  equal  to  the  lati- 
tude of  that  place. 

Let  i<  be  a  place  on  the 
earth  PEpQ,  Pp   being 
the  earth's  axis  and  EQ'\^ 
equator.     Z  is  the  zenith  of 
the  place,  and  HR  its  hori- 
zon.   X  0  C  is  the  latitude 
of  L  according  to  ordinaiy 
geographical  definitions;  t.0.> 
it  is  the  angular  distance  of 
L  from  the  equator.    Pro-  __^_^_^ 
long  OP  indefinitely  to  P'  '»»•"• 

and  draw  LP'  parallel  to  it,    P'  and  P'  ate  pomts  on 
the  celestial  sphere  infinitely  distant  from  h.    In  fact 
they  appear  as  me  point  since  the  dimension  of  the  wth 
are  vanishingly  small  compared  vith  the  radius  of  the 
celestial  sphere,  which  may  be  taktn  as  large  as  we  please. 
We  have  then  to  prove  that  LOQ=P'LB.    PO^ 
and  ^i  Fare  right  angles,  and  therefore  equal.    ZLP^ 
=  ZOP'  by  construction.    Hence  ZLH-  ZLP  — 
POQ-  ZOP',oT  the  latitude  of  the  point  L  is  meafr 
uwd  by  either  of  the  equal  angles  LOQoxP'ltff* 


k[ 


-. +->*;J»iV.-'-i''WS^- 


•■^mr '  >- 


huj^ 


I ![ 


$H  ABTRONOMT. 

If  we  denote  the  latitude  by  q>  it  follows  that  the  N.  P.D. 
(north-polar  distance)  of  Z  is  90°  —  g>.  As  an  observer 
moves  to  various  parts  of  the  earth,  his  senith  changes 
position  with  him.  In  every  position  the  N.P.D.  of  his 
lenith  is  90°  —  q>.  If  he  is  at  the  equator  his  ^  is  0°  and 
his  zenith  is  90°  from  the  north  pole,  which  must  there- 
fore be  in  his  horizon.  If  he  is  at  the  north  pole,  q>  —  ■\- 
90°  and  the  N.P.D.  of  his  zenith  is  0°,  or  his  zenith  co- 
incides with  the  north  pole.  If  he  is  at  the  sonth  polo 
{tp=  -  90°)  the  N.P.D.  of  his  zenith  is  90°  -  (-  90°) 
or  180°.  That  is,  his  zenith  is  180°  from  the  north  pole, 
or  it  must  coincide  with  the  sonth  pole ;  and  so  in  other 
oases. 

All  this  has  just  been  shown  (pages  38-30)  in  another 
way,  but  it  is  of  the  first  importance  that  it  should  be  not 
only  dear  but  familiar  to  the  student.  When  he  sees  any 
astronomical  diagram  in  which  the  north  pole  and  the  hori- 
son  are  laid  down  he  can  at  once  tell  for  what  latitude  this 
diagram  is  constructed.  The  elevation  of  the  pole  above 
the  horizon  measures  the  latitude  of  the  observer,  to  whose 
station  this  particular  diagram  applies. 

Change  of  the  Position  of  the  Zenith  of  an  Obsermr  by 
the  Diiinal  Motion.— In  Fig.  12  suppose  nesqia  repre- 
sent the  earth  and  NE  8  Q  the  celestial  sphere.  The  earth, 
as  we  know,  is  rotating  on  the  axis  NS.  We  have  now  to 
inquire  what  are  the  real  circumstances  of  this  motion. 
The  apparent  phenomena  have  been  previously  described. 
Bemember  that  the  vertical  line  of  an  observer  is  (practi- 
cally) that  of  a  radius  of  the  earth  passing  through  his 
station.  If  the  observer  is  at  n  his  zenith  is  at  N.  As 
the  earth  revolves  the  zenith  will  revolve  also.  If  the  ob- 
server is  in  45°  north  latitude,  he  is  carried  ronnd  b^  the 


■-,  ■'■^■'^>$^-\^^^¥^/0^i'i^'''fi'<'4 


i.i%-;L.'-;i-^i'M?i.% 


t  the  N.P.D. 
I  an  observer 
inith  ohangei 
T.P.D.  of  his 
is  9»  ifl  0°  and 
,  most  there- 
pole,  <p-  + 
lis  xenith  oo- 
le  south  polo 
r  -  (-  90°) 
e  north  pole, 
so  in  other 

))  in  another 
should  be  not 
1  he  sees  any 
and  the  hori- 
i  latitude  this 
he  pole  above 
Ter,  to  whose 

lObterrer  by 

esq  to  repre- 
.  The  earth, 
I  have  now  to 
this  motion, 
sly  described, 
er  is  (practt- 
throngh  his 
is  at  K  Am 
.  If  the  ob- 
ronnd  b^  the 


aSLATION  OF  THB  XABTH  TO  THB  HBAVEN8.  38 

lolation  of  the  earth  in  a  small  circle  of  the  earth's  surface 
whose  ptane  is  perpendicular  to  the  earth's  axis.  This  is 
the  paraUel  of  46°,  so  called,  and  is  indicated  in  the  figure. 
His  zenith  is  always  directly  above  him,  and  therefore  his 
zenith  must  describe  each  day  a  circle  ML  on  the  celestial 
sphere  corresponding  to  this  parallel  on  the  earth;  that  is, 


Wm.1k 

a  circle  half  way  between  the  celestial  pole  and  the  celestial 
equator.  Now,  suppose  the  observer  to  be  on  the  equator 
eq.  His  zenith  wiU  then  be  90°  from  either  pole.  As  the 
earth  revolves  on  its  axis  his  zenith  will  describe  a  great 
circle  EQon  thecelestial  sphere.  This  cirr'e  is  the  celestial 
equator.    An  observer  at  45°  soiith  Uit.    4*  wiU  h*ve  $ 


"'-'r^"m^v5mm-'!^-!!'S^- 


mmm 


f  i 


84 


A8TR0N0MT. 


parallel  80  marked  oat  on  the  celestial  sphere  by  the 
motion  of  his  zenith  due  to  the  earth's  rotation,  and  so  on. 
Thus,  for  each  parallel  of  latitnde  on  the  earth  we  have  a 
corresponding  circle  on  the  celestial  sphere,  and  each  of 
these  latter  circles  has  its  poles  at  the  celestial  poles. 

Not  only  are  there  circles  of  the  celestial  sphere  which 
correspond  to  parallels  of  latitude  on  the  earth,  but  there 
are  also  celestial  meridians  corresponding  to  the  yarions 
terrestrial  meridians.    The  plane  of  the  meridian  of  any 
place  contains  the  zenith  of  that  place  and  the  two  celestial 
poles.     It   cuts  from  the  earth's   surface  the  terrestrial 
meridian  and  from  the  celestial  sphere  that  great  circle 
which  we  hare  defined  as  the  celestial  meridian.    T'«  fix 
the  ideas  let  as  suppose  an  obserrer  at  some  one  point  of 
the  earth's  surface.    A  north  and  south  line  on  the  earth 
at  that  point  is  the  visible  representative  of  his  terrestrial 
meridian.    A  plane  through  the  centre  of  the  earth  and 
that  line  contains  his  zenith,  and  cuts  from  the  celestial 
sphere  the  celestial  meridian.    As  the  earth  rotates  on  its 
axis  his  zenith   moves  around  the  celestial  sphere  in  a 
parallel  as  Z£  in  the  last  figure.    Suppose  that  the-  east 
point  is  in  front  of  the  picture,  the  west  point  being  be- 
hind it.    Then  as  the  earth  rotates  the  zenith  Z  will  move 
along  the  line  ZL  from  Z  towards  L.    The  celestial  meri- 
dian always  contiuns  the  celestial  poles  and  the  point  Z, 
wherever  it  may  be.    Hence  the  arcs  of  great  circles  join- 
ing N.P.  and  8.P.  in  the  figure  are  representatives  of  the 
celestial  meridian  of  this  observer,  at  different  times  dur- 
ing the  period  of  the  earth's  rotation.    They  have  been 
drawn  to  represent  the  places  of  the  meridian  at  intervals 
of  1  hour.    That  is,  13  of  them  are  drawn  to  represent 
13  QoqBeoutiYe  positioiw  of  the  meridian  daring  a  sem^ 


sphere  by  the 
on,  and  bo  on. 
jrth  we  have  a 
),  and  each  of 
ial  poles. 
1  sphere  which 
rth,  but  there 
to  the  various 
eridian  of  any 
le  two  celestial 
the  terrestrial 
at  great  circle 
idian.    T'«  fix 
>  one  point  of 
e  on  the  earth 
his  terrestrial 
the  earth  and 
n  the  celestial 
L  rotates  on  its 
ftl  sphere  in  a 
that  the-  east 
loint  being  bo- 
th Z  will  move 
» celestial  meri- 
id  the  point  Z, 
sat  circles  join- 
intatiTes  of  the 
rent  times  dur- 
[^heyhave  been 
ian  at  interrals 
^n  to  represent 
daring  a  8emi« 


RELATION  OF  TUB  EARTH  TO  TUB  UEAVEHS.   36 

revolution  of  the  earth.    In  this  time  Z  moves  from  Z  to 
L.    In  the  next  semi-revolution  Z  moves  from  L  to  Z, 
along  the  other  half  of  the  parallel  ZL.    In  24  hours 
the  zenith  Z  of  the  observer  has  moved  from  Zto  L  and 
from  L  back  to  Z  again.    The  celestial  meridian  has  also 
swept  across  the  heavens  from  the  position  N.P.,  Z,  Q,  S, 
S.P.  through  every  intermediate  position  to  N.P.,  L,  E,  0, 
S.P.,  and  from  this  last  position  back  to  N.P.,  Z,  Q,  S, 
S.P.    The  terrestrial  meridian  of  the  observer  has  been 
under  it  all  the  iime.    This  real  revolution  of  the  celestial 
meridian  is  incessantly  repeated  with  every  revolution  of 
the  earth.    The   sky  is  studded  with  stars  all  over  the 
sphere.    The  celestial  meridian  of  any  place  approaches 
these  various  stars  from  the  west,  passes  them,  and  leaves 
them.    This  is  the  real  state  of  things.    Apparently  the 
observer  is  fixed.    His  terrestrial  and  celestial  meridians 
seem  to  him  to  be  fixed,  not  only  with  reference  to  himself, 
as  they  are,  but  to  be  fixed  in  space.    The  stars  appear  to 
him  to  approach  his  celestial  meridian  from  the  east,  to 
pass   it,  and  to  move  away  from  it   towards   the  west. 
When  a  star  crosses  the  celestial  meridian  it  is  said  to 
culminate.    The  passage  of  the  star  across  the  meridian  is 
called  the  transit  of  that  star.    This  phenomenon  takes 
place  successively  for  each  observer  on  the  earth.    Suppose 
two  observers,  A  and  B,  A  being  one  hour  (15°)  east  of 
B  in  longitude.    This  means  that  the  angular  distance  of 
their  terrestrial  meridians  is  15"  (see  page  10).    From  what 
we  have  just  learned  it  follows  that  their  celestial  mesi- 
dians  are  also  16°  apart    When  B's  meridian  is  N.P., 
Z,  Q,  R,  S.P.,  A's  will  be  the  first  one  (in  the  figure) 
beyond  it;  when  B's  meridian  has  moved  to  this  first  posi- 
tion, A's  will  be  in  the  second,  and  so  on,  always  16* 


,lf  I 


w 


ASTRONOMY. 


(1  honr)  in  advance.  A  group  of  stars  which  has  jnst  como 
to  A's  meridian  will  not  pass  B's  for  1  hoar.  When  they 
are  on  B's  meridian  they  will  bo  1  hour  west  of  A's,  and 
so  on.  Notice  also  that  A's  zenith  is  always  15"  east  of 
B's. 

The  same  stars  will  succeFsively  rise,  calminate,  and  set 
to  each  observer,  but  tlie  phenomena  will  be  presented  to 
the  eastern  observer  sooner  than  to  the  other. 


I ' 

»•         « 


hag  jnat  cnmo 

Wht'ii  they 

si  of  A's,  and 

|ra  15"  east  of 

inate,  and  set 
presented  to 


CHAPTER  n. 

THE  RELATION  OP  THE  EARTH  TO  THE  HEAVENS- 

{OonUnutd.) 

Tn  CSUCTIAL  Bphui. 

gygtemi  of  Oo-ordinatea— The  great  circles  of  the  celestial 
sphere  which  pass  through  the  two  celestial  poles  are  called 
hour-eirdea.  Each  hour-circle  is  the  celestial  meridian  of 
some  place  on  the  earth. 

The  honr-oirole  of  any  partionlar  star  is  that  one  which 
passes  through  the  star  at  the  time.  As  the  earth  revolves, 
different  honr-droles,  or  celestial  meridians,  come  to  the 
star. 

In  Fig.  18  l«t  0  be  the  position  of  the  earth  in  the  centre  of 
the  celestial  iphwe  2fZ  8D.  Let  Zbe  the  zenith  of  the  ob- 
server at  a  given  instant,  and  P,  p^  the  celestial  poles.  By 
definition  PZSpnNP  is  his  celestial  meridian.  (Each 
of  these  points  hits  a  name;  let  the  student  give  the  names 
in  order.)  N8'\%  the  horizon  of  the  observer  at  the  instant 
chosen.  PO  JV^  is  his  latitude.  If  P  is  the  north  pole,  he 
is  in  latitude  34°  north.    (See  page  31.) 

EC  WD  is  the  celestial  equator;  J? and  W  are  the  east 
and  west  points.  The  earth  is  turning  from  WUtB.  That 
is,  the  celestial  meridian  which  at  the  instant  chosen  in  the 
picture  oontains  P  Zp  was  in  the  position  P  D  Rp  twelve 
bonrs  earlier. 


gg  ASTRONOMY. 

PV,  PB,  PV,  PD  lire  parts  of  hour-circlos.  If  A  is 
a  sUir,  7'  B  is  tho  hour-circle  of  that  star.  As  the  eartli 
tiiriw  P  B  turns  with  it,  and  directly  P  B  will  have  moved 
away  from  A  towards  liio  top  of  tho  picture  and  soon  /'  V 
will  pass  through  the  star  A,  which  stands  still.  When  it 
does,  PV  will  be  the  hour-circle  of  A.  At  the  instant 
chosen  PB  U  the  hour-circle  of  A.  The  atars  inside  the 
circle  NK  are  always  above  the  obaenrer'g  horizon.    Im  ia 


ill! 


half  of  the  dinmal  orbit  of  one  of  the  north  stars.  All  the 
stars  inside  the  circle  <S'^  are  perpetually  invisible  to  the 
observer,  o  r  is  half  of  the  orbit  of  one  of  these  southern 
stars.  The  north-polar  distance  of  all  those  stars  perpetu- 
ally above  the  horizon  is  less  than  or  equal  toPJV;  the 
south-poUr  distance  of  all  the  stars  perpetually  invisible  is 
less  than  or  equal  to  ;i  i9,  which  is  equal  to  FN, 


Ui 


BBLATION  OF  TIOB  SARTH  TO  TBB  HEAVENS.  80 


■clos.  If  A  is 
As  tho  oarth 
illhttvo  moved 
I  and  soon  P  V 
liill.  When  it 
kt  the  instant 
liars  inside  the 
torizon.    /  m  ia 


stars.  All  the 
invisible  to  the 
these  southern 
i  stars  perpetu- 
al to  PJV;  the 
lally  inyisible  ia 
FN, 


Altitude  and  Atimuth.— Z^?  is  the  rertical  circle  of  the 
star  A  at  the  instant  cliosen  for  making  the  picture.  In 
a  few  moments  Z  will  have  moved  eastwards  and  a  new 
vertical  circle  will  have  to  be  drawn.  OA  is  the  altitude 
of  A  at  the  instant;  in  a  few  moments  it  will  be  less.  For 
as  Z moves  towards  the  eastward,  NWS,  the  western  hori- 
zon of  the  observer,  will  move  upwards  (in  the  drawing) 
and  come  nearer  to  A,  which  stands  still.  Therefore  the 
altitude  of  A  will  diminish  progressively.    It  is  now  OA. 

The  azimuth  of  A  is  now  NO,  counted  from  the  north 
point.  It  will  change  as  Z  changes.  Having  the  altitude 
and  azimuth  of  A  at  the  instant,  the  observer  at  0  can  find 
it  in  tho  sky.     (See  page  18.) 

Horth-Polar  Diitanee  and  Hour-Angle.— The  north-polar 
distance  of  A  in  PA.  This  will  serve  as  one  of  a  pair  of 
co-ordinates  to  point  out  the  apparent  position  of  A  in  the 

sky. 

The  hour-angle  of  a  star  i»  the  angular  distance  between 
the  celestial  meridian  of  the  place,  and  the  hour-circle  of 
that  star.  The  hour-angle  is  counted  from  the  meridian 
towards  the  west  from  0°  to  360°,  or  from  0*  to  24*.  The 
hour-angle  of  A,  at  this  instant,  is  ZPB.  The  hour- 
angle  of  a  star  A'  is  0°. 

The  hour-angle  is  measured  by  th<i  arc  of  the  equator 
between  the  celestial  meridian  and  the  foot  of  the  hour- 
circle  through  the  star.  The  are  CB  measures  the  hour- 
angle  of  A  at  the  instant.  Directly,  Z  will  have  moved  away 
to  tho  east  and  O  will  move  away  also  along  the  dotted  part 
of  the  line  representing  the  equator,  WCED. 

Having  the  two  co-ordinates  PA  and  CB,  the  obeerver 
at  0  can  find  the  star  A.  It  will  be  noticed  that  these  two 
oo-ordinates,  polar  distance  and  hour-angle,  differ  in  one 


■'wrr. 


T 


[I 

;   1 

.   1 

1  \, 

1  i 

'  1 

ii 

■  '-■ 

•'■ 

40 


ASTROyOMT. 


rsBf  )ot  from  the  two  co-ordinatea  altitude  and  asimnth. 
Both  the  latter  change  oa  the  earth  revoWos  on  ita  axia.  Of 
the  former  only  one  ohnngea;  tii.,  the  hour-angle.  The 
polar  dictanco  of  a  atar  rcmaina  the  aome,  ainoe  it  ia  the  dia- 
timc(!  from  a  flxod  point,  the  pole,  to  a  fixed  point,  the  atar. 

Kight  AaotnaioB  and  Vorth-Polar  SiataaM.— We  can 
deviao  a  pair  of  co-ordinatea  tmlher  of  which  ahall  change 
aa  the  earth  revoWea.  Thia  will  dearly  be  conyenient,  for 
thia  pair  of  co-ordinatea  will  be  the  aame  for  etery  ebaerrer 
and  for  every  hour  of  the  day,  whereaa  the  others  Tary  with 
the  time,  and  with  the  aitnation  of  the  obaerrer. 

To  aeleot  auch  a  pair  we  have  aimply  to  nae  fixed  pointa 
in  the  celeatial  sphere  to  count  from.  The  north  pole  will 
do  for  one  of  theae,  and  the  north-polar  diatance  of  the  atar 
will  lerTO  for  one  co-ordinate.  Thia  ia  meaanred,  for  the 
itar  A,  on  the  honr-oirole  PB.  Let  ua  chooae  aome  fixed 
point  V  oa  the  equator  to  meaanre  oar  other  co-ordinate 
from,  and  let  aa  always  meaanre  it  on  the  equator  towarda 
the  eaat  from  0**  to  860°  (from  0*  to  S4^).  That  ia,  from 
V  through  B,  G,  E,  D,  W,  anooessitely. 

F^  ia  the  right  a$cenaioH  of  A.  The  right  tuemmoH  of 
a  itar  ia  the  angular  distance  of  the  foot  of  th«  hour-eirele 
through  the  atar  from  the  vernal  equinox,  mooiured  on  the 
eeleatial  equator,  towarda  the  eaat. 

Exactly  what  the  yemal  eqainoz  is  we  shall  find  oat 
later  on;  for  the  present  it  ia  anificient  to  define  it  as  a 
certain  fixed  point  on  the  celestial  eqaator. 

1  ■'e  have  the  right  ascension  and  north-polar  distanoe 
of  a  star,  we  can  point  it  oat.  Thns  VB  and  PA  define 
the  position  of  A.  As  long  aa  the  pole,  the  atar,  and  the 
Temal  equinox  do  not  more  relatiyely  to  each  other  these 
two  co-ordinatea  fix  the  position  of  the  star.    Their  relatiye 


;tUi 


BKLATION  OF  THE  BAHTU  TO  TUB  HBAVBNB.  41 


and  asimnth. 
>n  its  axil.  Of 
ir-angle.  The 
io«  it  ii  the  dif- 
[mint,  the  atar. 
Aoa.— We  can 
h  ahall  change 
wnyenient,  for 
etery  ebaerfer 
then  Tary  with 
rrer. 

M  fixed  pointa 
north  pole  will 
race  of  the  atar 
lanred,  for  the 
ose  aome  fixed 
ler  co-ordinate 
qnator  towarda 

That  ia,  from 

rA<  MCMMtMl  of 

th»  hour-eireh 
\ea$ured  on  th« 

ahall  find  oat 
)  define  it  aa  a 

-polar  diatanoe 
»ni  PA  define 
te  atar,  and  the 
ich  other  theae 
Their  relatiTe 


poaitiona  are  not  aftected  by  the  rotation  of  the  earth,  nor 
by  the  poaition  of  the  obeerver  upon  its  aarfaoe.  He  may 
be  in  any  latitude  or  any  longitude,  and  hia  aenith  may  be 
anywhere  in  the  whole  aky,  but  the  right  aaoenaion  and 
the  north-polar  diatanoe  of  each  atar  remain  the  lame  ne?* 
ertheleaa. 

The  right  aaoenaion  of  the  atar  KiiVC.  Of  a  atar  at  J7 
it  ia  VCE;  of  a  atar  at  Z>  it  i»  VCED\  of  a  star  at  IT 
it  ia  V  CED  W,  and  ao  on. 

ligL.  Aaoenaion  and  Declination. — Sometimea  in  place 
of  the  north-pokr  diatanoe  of  a  atar  it  ia  convenient  to 
nae  ita  declination. 

Th»  declination  of  a  star  is  its  angular  distance  north  or 
touth  of  the  celestial  equator. 

The  declination  of  ^  ia  BA,  which  ia  90**  minus  PA. 

The  rebition  between  N.  P.  D.  and  d  ia 

N.  P.  D.  =  90"  -  *;    d  =  90»  -  N.  P.  D. 

North  deolinationa  are  +;  South  deolinationa  are  — . 

The  declination  ot  Z  in  CZ.  CZia  equal  to  P  Jf,  ainco 
each  ia  equal  to  90°  —  PZ.  PN  meaaurea  the  latitude  of 
the  obaerrer  whoae  zenith  ia  Z.   (See  page  81.) 

The  latitude  of  a  place  on  the  earth's  surface  is  measured 
by  the  declination  of  tts  tenith. 

Thia  ia  the  definition  of  the  latitude  which  ia  need  in 
aatronomy. 

Oomrdiaatea  of  a  Star.— In  what  haa  gone  before  we  have 
Been  that  there  are  Tarioua  waya  of  expreaaing  the  apparent 
positions  of  stars  on  the  aurfiwe  of  the  oeleatial  aphere. 
That  one  moat  commonly  oaed  in  astronomy  ia  to  gito  the 
right  ascension  and  north-polar  distance  (or  dedination)  of 
the  atar.    The  apparent  poaition  of  the  atar  ia  fixed  by  these 


;.'jt';&'-^...'jg5i-"- '  -'.--!-!-!."i-" 


43 


ASTBOyOMT. 


If! 
>■   1 


two  co-ordinates.  If  we  know  its  distance  also,  the  afoso* 
lute  position  of  the  star  in  space  is  fixed  by  the  three  co- 
ordinates. Thus  we  hare  a  complete  method  of  describing 
the  positions  of  the  heavenly  bodies. 

Co-ordinates  of  aik  Obserrer. — ^To  describe  the  position  of 
an  obserrer  on  the  surface  of  the  earth  we  have-  to  giye  his 
latitnds  and  longitnde.  His  latitude  is  the  declination  of 
his  zenith;  his  longitude  is  the  fixed  angle  between  his 
celestial  meridian  and  the  celestial  meridian  of  Greenwich 
(or  Washington).  Declination  in  the  sky  is  analogous  to 
Latitude  on  the  earth.  Bight  ascension  in  the  sky  is  anal- 
ogous to  Longitude  on  the  earth.  Both  of  these  co-ordi- 
nates depend  upon  the  position  of  his  zenith,  since  his 
longitnde  is  nothing  but  the  angular  distance  of  his  zenith 
west  of  the  zenith  of  Greenwich. 

All  this  is  extremely  simple,  but  if  it  is  clearly  under- 
stood the  student  has  it  in  his  power  to  answer  a  great 
many  interesting  questions  for  himselt 

We  know,  for  example,  that  the  sun  is  in  the  equator  and  at  the 
Yernal  equinox  on  March  2l8t  of  each  year. 

The  student  can  determine  for  himself  what  appearances  will  be 
presented  on  that  day  next  year.  He  may  proceed  in  this  way:  Draw 
a  circle  to  reprtdeut  the  celestial  sphere.  Take  a  point,  P,  of  it  to 
be  the  position  of  the  north  pole  in  the  sky.  If  the  observer  lives 
In  a  phice  whose  latitude  is  g>  degrees  north,  his  zenith  will  be 
90°  —  ^  from  the  north  pole  measured  towards  the  south.  Measure 
oft  90°  —  9>  on  the  circle  from  P.  The  end  of  that  arc  is  the  zenith 
of  that  observer,  Z.  PZ  is  an  arc  of  his  celestial  meridian.  Meas- 
ure from  P  through  Z  90*,  and  the  end  of  that  are  is  on  the  eqqator, 
Q  say.  Join  P  with  the  centre,  0,  of  the  circle.  This  line  is  the 
direction  of  the  celestial  pole.  Join  0  and  Q,  and  this  line  (perpen- 
dicuUr  to  PO)  is  the  direction  of  that  point  of  the  equator  which  is 
highest  above  his  horizon.  Draw  the  line  ZO;  this  is  the  vertical 
line.  Throu^O  draw  JIT  0^  perpendicular  to  ZO.  This  is  the  north 
and  south  line  of  bis  horizon.    Draw  the  ovals  which  repreeent  (in 


BELATION  OF  THE  EABTB  TO  THE  HSAVENa.  43 


Iso,  the  afoso< 
the  three  oo- 
of  describing 

lie  position  of 
re  to  giyehis 
leclination  of 
between  his 
of  Greenwich 
analogoQS  to 
le  sky  is  aual- 
;hese  co-ordi- 
ith,  since  his 
of  his  zenith 

learly  nnder- 
iswer  a  great 

lator  «nd  at  the 

larances  will  be 
Ihisway:  Draw 
loint,  P,  of  it  to 
I  observer  lives 
zenith  will  be 
DUth.  Measure 
arc  is  the  zenith 
eridian.  Meas* 
on  the  eq^ator, 
rhia  line  is  the 
lis  line  (perpen- 
[uator  which  is 
I  is  the  Tertioal 
Phis  is  the  north 
>h  represent  On 


perspective)  the  circles  of  the  equator  and  of  the  horizon.  Assume 
rpoint,  V,  of  the  celestial  equator.  On  March  21st  of  each  year  the 
sun  is  there.  When  the  sun  is  at  the  highest  point  Q  of  the  equatoi 
it  is  noon  to  this  observer.  The  sun  is  on  Ms  meridian.  Six  houw 
before  this  time  the  sun  will  rise  to  him;  six  hours  after  he  will 
set  It  requires  twenty-four  hours  for  the  point  F  to  be  apparently 
carried  all  round  the  equator,  and  the  sun  appears  to  go  with  the 
poinC  Three  months  later  the  sun  is  about  fiO°  of  right  ascension 
and  has  a  north-polar  distance  of  8<H*.  The  student  can  determine 
in  the  same  way  the  circumstances  under  which  the  sun  will  appear 
to  him  to  move  on  the  21st  of  next  June  when  ito  north-polar  distance 

is  66i° 

The  example  that  te  here  given  is  not  for  the  purpose  of  teaching 
the  student  what  tLe  motion  of  the  sun  is;  that  will  be  considered  in 
iU  proper  order  in  this  book.  But  it  is  to  show  him  that  if  he  wishes 
to  know  about  it  he  can  find  out  for  himself. 

When  he  reads  about  the  midnight  sun  that  is  visible  in  the  Arctic 
regions  he  can  verify  the  facU  for  himself.  Let  him  constract  the 
diagram  we  have  described  for  a  place  whose  latitude  is  80  north 
and  see  what  sort  of  a  diurnal  orbit  the  suu  wlU  describe  on  the  21st 
of  June  when  lU  N.  P.  D.  is  66i*. 

BuATKHi  or  Ton  to  thi  Sphui. 
Sidereal  Time.— The  earth  rotates  nniformly  on  its  axis; 
that  is,  it  turns  through  equal  angles  in  equal  intervals  of 

time. 

This  rotation  can  be  used  to  meanire  any  interrals  of 
time  when  once  a  unit  of  time  is  agreed  upon.  The  most 
natural  and  convenient  unit  is  a  day.  There  aw  various 
kinds  of  days,  and  we  have  to  take  them  as  they  are. 

A  sidereal  day  it  the  interval  of  time  required  for  th» 
tarth  to  rotate  once  on  its  axis.  Or  what  is  the  same  thing, 
it  is  the  interval  of  time  between  two  consecutive  tran- 
dts  of  any  star  over  the  same  celestial  meridian.  The 
sidereal  day  is  divided  into  24  sidereal  hours;  each  hour  is 
divided  into  60  minutes;  each  minute  into  60  seconds.  In 
makine  one  revolution  the  earth  turns  through  860',  so  that 


jaam-'-!." 


44 


AffTRONOMT. 


hi 

i;  !l 


11  : 


I.  ; 
t 


24  hours  =  360°;  also, 

1  hour  =  15°;  1°  =  4  minntes. 
1  minute  =  15';  I'  =  4  seconds. 
1  second  =  15';  1'  =0.066  second. 

When  a  star  is  on  the  celestial  meridian  of  any  place  its 
hour-angle  is  zero,  by  definition  (see  page  39).  It  is  then 
at  its  transit  or  culmination. 

As  the  earth  rotates,  the  meridiaa  moves  away  (east- 
wardly)  from  this  star,  whose  hour-angle  continually  in- 
creases from  0°  to  360°,  or  from  0  hours  to  24  hours. 
Sidereal  time  can  then  be  directly  measured  by  the  hour- 
angle  of  any  star  in  the  heavens  which  is  on  the  meridian 
at  an  instant  we  agree  to  call  sidereal  0  hours.  When  this 
star  has  an  hour-angle  of  90°,  the  sidereal  time  is  6  hours; 
when  the  star  has  an  hour-angle  of  180°  (and  is  again  on 
the  meridian,  but  invisible  n^lpss  it  is  a  circumpolar  star),  it 
is  12  hours ;  when  its  hott.  -hi>  '^  i?  270°,  the  sidereal  time 
is  18  hours;  and,  finally,  wh  e  itar  reaches  the  upper 
meridian  again,  it  is  24  houi\^  o«-  0  hours.  (See  Fig.  13, 
where  E  O  WD  is  the  apparent  diurnal  {wth  of  a  star  in 
the  equator.    It  is  on  the  meridian  at  C.) 

Instead  of  choosing  a  $tar  as  the  determining  point 
whose  transit  marks  sidereal  0  hours,  it  is  found  more  con- 
▼enient  to  select  that  point  in  the  sky  from  which  the  right 
ascensions  of  stars  are  counted — the  yemal  equinox — the 
point  V  in  the  figure.  The  fundamental  theorem  ol  si- 
dereal time  is:  The  hour-atigle  of  tie  vernal  equinox,  or  the 
sidereal  time,  ie  equal  to  the  right  aeeensum  of  the  meri- 
dian; that  is,  CV^VG. 

To  aroid  coniinnal  reference  to  the  stars,  we  set  a  clock 
so  that  its  hands  shall  mark  0  hours  0  minntes  0  seoondi 


.MM 


BSLATtOlt  OF  TBM  MARTU  TO  TUB  HEAVBNa.  46 


d. 


any  place  its 
It  is  then 


')' 


IS  away  (east- 
ontinnally  in- 
to 24  honrs. 
by  the  honr- 
the  meridian 
When  this 
me  is  6  hoars; 
1  is  again  on 
apolar  star),  it 
)  sidereal  time 
hes  the  upper 
(See  Fig.  18, 
I  of  a  star  in 

mining  point 
tnd  more  con- 
hich  the  right 
equinox — the 
leorem  of  d- 
jMitMx,  or  the 
0/  the  meri- 

re  set  a  dock 
itesOieoondf 


at  the  transit  of  the  vernal  equinox,  and  regulate  it  so  that 
its  hour-hand  reyolves  once  in  24  sidereal  hours.  Such  a 
clock  is  called  a  sidereal  clock. 

Solar  Time. — Time  measured  by  the  hour-angle  of  the 
sun  is  called  true  or  apparent  solar  time.  An  apparent 
solar  day  is  the  interval  of  time  between  two  consecutive 
transits  of  the  sun  over  the  upper  meridian.  The  instant 
of  the  transit  of  the  sun  over  the  meridian  of  any  place 
is  the  apparent  noon  of  that  place,  or  local  apparent  noon. 

When  the  sun's  hour-angle  is  12  honrs  or  180%  it  is 
local  apparent  midnight. 

The  ordinary  sun-dial  marks  apparent  solar  time.  As 
a  matter  of  fact,  apparent  solar  days  are  not  equal  The 
reason  for  this  will  be  fully  explained  later.  Hence  our 
docks  are  not  made  to  keep  this  kind  of  time,  for  if  once 
set  right  they  would  sometimes  lose  and  sometimea  gain 
on  such  time. 

Ibaa  Bdar  Time. — A  modified  kind  of  solar  time  is 
therefore  used,  called  mean  eolar  time.  This  is  the  time 
kept  by  ordinary  watches  and  docks.  It  is  sometimes 
oaUed  civil  time.  Jfean  solar  time  is  measured  by  the  hour- 
angle  of  the  mean  sun,  a  fictitious  body  which  is  imagined 
to  move  uniformly  in  the  heavens.  The  law  according  to 
which  the  mean  sun  is  supposed  to  move  enables  us  to  com- 
pute its  exact  position  in  the  heavens  at  any  instant,  and  to 
define  this  position  by  the  two  co-ordinates  right  asoensi<m 
and  declination.  Thus  we  know  the  position  of  this  imagi- 
nary body  just  as  we  know  the  position  of  a  star  whose 
oo-wdinates  are  given,  and  we  may  speak  of  its  iransit  as 
if  it  were  a  Imght  material  point  in  the  sky.  A  mean 
Misr  day  is  the  interval  of  time  between  two  consecutive 
tnuMnts  of  the  mean  sun  over  the  upper  meridian.    Meam 


'!-;; 


1 


■  ^.WJ).!li.r!'V.iJ;^..-!ttUJ"t.m'IK!W.'.. 


46 


ASTRONOMY. 


noon  at  any  place  on  the  earth  is  the  instant  of  the  mean 
sun's  transit  over  the  meridian  of  that  place.  Twelve  hours 
after  local  mean  noon  is  local  mean  midnight.  The  mean 
solar  day  is  divided  into  24  hours  of  60  minutes  each.  Each 
minute  of  mean  time  contains  60  mean  solar  seconds. 
Astronomers  begin  the  mean  solar  day  at  noon,  which  is  0 
hours,  and  count  round  to  24  hours. 

We  have  thus  three  kinds  of  time.  They  are  alilte  in  one  point: 
each  is  measured  by  the  hour-angle  of  some  lK>dy,  real  or  assumed. 
The  body  chosen  determines  the  Itind  of  time,  and  the  alraolute  length 
of  the  unit — the  day.  The  simplest  unit  is  that  determined  by  tiie 
uniformly  rotating  earth — the  sidereal  day;  the  most  natural  unit  is 
that  determined  by  the  sun  itself — the  apparent  solar  day,  which, 
however,  is  a  variable  unit;  the  most  convenient  unit  is  the  mean 
solar  day,  and  this  is  the  one  chosen  for  use  in  our  daily  life. 

Comparatiye  Lengths  of  the  Mean  Solar  and  Sidereal 
Say. — As  a  fact  of  observation,  it  is  found  that  the  sun 
appears  to  move  from  west  to  east  among  the  stars,  about 
1°  daily,  making  a  complete  revolution  around  the  sphere 
in  a  year.    It  requires  365^  days  to  move  through  360". 

Hence  an  apparent  solar  day  will  be  longer  than  a  side- 
real day.  For  suppose  the  sun  to  be  at  the  vernal  equinox 
exactly  at  sidereal  noon  (0  hours)  of  Washington  time  on 
March  21st;  that  is,  the  vernal  equinox  and  the  sun  are 
both  on  the  meridian  of  Washington  at  the  same  instant. 
In  24  sidereal  hours  the  vernal  equinox  will  again  be  on  the 
same  meridian,  but  the  sun  will  have  moved  eastwardly  by 
about  a  degree,  and  the  earth  will  have  to  turn  through 
this  angle  and  a  little  more  in  order  that  the  sun  shall 
again  be  on  the  Washington  meridian,  or  in  order  that  it 
may  be  apparent  noon  on  March  22d.  For  the  meridian 
to  overtake  the  sun  requires  about  4  minutes  of  sidereal 


'i-4^j^'. 


9W^ 


RELATION  OF  THE  EARTH  TO  THE  UBAVBN8.  47 


of  the  mean 
Twelve  hours 
The  mean 
each.  Each 
>lar  seconds. 
n,  which  is  0 


in  one  point: 
tl  or  assumed, 
absolute  length 
ermined  by  the 
natural  unit  ia 
ar  day,  which, 
it  is  the  mean 
ily  life. 

lad  Sidsreal 
that  the  snn 

stars,  abont 
1  the  sphere 
ugh  360^ 
than  a  side- 
irnal  equinox 
ton  time  on 

the  sun  are 
ame  instant 
oin  be  on  the 
iastwardlv  by 
mm  through 
he  snn  shall 
order  that  it 
the  meridian 
B  of  sidereal 


time.  Th«  true  sun  does  not  move,  as  we  have  said,  uni- 
formly. The  mean  sun  is  supposed  to  move  uniformly, 
and  to  make  the  circuit  of  the  heavens  in  the  same  time  as 
the  real  sun.  Hence  a  mean  solar  day  will  also  be  longer 
than  a  sidereal  day,  for  the  same  reason  that  the  apparent 
solar  day  is  longer.    The  exact  relation  is: 


1  sidereal  day  = 

24  sidereal  hours  = 

1  mean  solar  day  = 

24  mean  solar  hours  = 


0-997  mean  solar  day. 

23h  SO"  4* -091  mean  solar  time, 
1-003  sidereal  days, 

34i>  S{"  66*-555  sidereal  time, 


and 


866-24222  sidereal  days  =  865-24222  mean  solar  days. 

Local  Time.— When  the  mean  sun  is  on  the  meridian  of 
a  place,  as  Boston,  it  is  mean  noon  at  Boston.  When  the 
mean  sun  is  on  the  meridian  of  St.  Louis,  it  is  mean  noon 
at  St.  Louis.  St.  Louis  being  west  of  Boston,  and  the 
earth  rotating  from  west  to  east,  the  local  noon  of  Boston 
occurs  before  the  local  noon  at  Tt.  Louis.  In  the  same 
way  the  local  sidereal  time  at  Boston  at  any  given  instant 
is  expressed  by  a  larger  number  than  the  local  sidereal  time 
of  St.  Louis  at  that  instant. 

The  sidereal  time  of  mean  noon  is  given  in  the  astro- 
nomical ephemeris  for  every  day  of  the  year.  It  can  be 
found  within  ten  or  twelve  minutes  at  any  time  by  remem- 
bering that  on  March  21st  it  is  sidereal  0  hours  about 
noon,  on  April  21st  it  is  about  two  hours  sidereal  time  at 
noon,  and  so  on  through  the  year.  Thus,  by  adding  two 
hours  for  each  month,  and  four  minutes  for  each  day  after 
the  2lBt  day  last  preceding,  we  have  the  sidereal  time  at 
the  noon  we  require.  Adding  to  it  the  number  of  hours 
since  noon,  and  one  minute  more  for  every  fourth  of  a  day 


***^';v',.':  >!i'^''-  ^yl'-;Ji^'!■'?*'^"■'■'i■-SJ?-;^^^l!^ 


48 


ASTRONOMT. 


on  account  of  the  constant  gain  of  the  clock  (4"  dailj),  we 
have  the  sidereal  time  at  any  moment. 

iirampfo.— Find  the  Bidereal  time  on  July  4th,  1881,  at  4  o'clock 
A.M.    Wc  have: 

k     m 

June  21st,  8  mouths  after  March  Slst;  to  be  X  3,  6    0 

July  8d,  12  days  after  June  2l8t;  X  4,  0  48 

4  A.1I.,  10  hours  after  noon,  aeasXy  f  of  a  day,  10    8 

This  result  is  within  a  minute  of  the  exact  Talue. 

Belation  of  Time  and  Longitude. — Considering  our  civil 
time  which  depends  on  the  sun,  it  will  be  seen  that  it  is 
noon  at  any  and  every  place  on  the  earth  when  the  sun 
crosses  the  meridian  of  that  place,  or,  to  speak  with  more 
precision,  when  the  meridian  of  the  place  passes  under  the 
sun.  In  the  lapse  of  24  hours  the  rotation  of  the  earth  on 
its  axis  brings  all  its  meridians  under  the  sun  in  succession, 
or,  which  ia  the  same  thing,  the  sun  appears  to  pass  in  suc- 
cession over  all  the  meridians  of  the  earth.  Hence  noon 
continually  travels  westward  at  the  rate  of  15°  in  an  hour, 
making  the  circuit  of  the  earth  in  24  hours.  The  differ- 
ence  between  the  time  of  day,  or  the  local  time  as  it  is  called, 
at  any  two  places  will  be  in  proportion  to  their  difference 
of  longitude,  amounting  to  one  hour  for  every  15  degrees  of 
longitude,  four  minutes  for  every  degree,  and  so  on.  Vict 
versa,  if  at  the  same  real  moment  of  time  we  can  deter- 
mine the  local  times  at  two  different  places,  the  difference 
of  these  times  multiplied  by  15  will  give  the  difference  of 
longitude. 

The  longitudes  of  places  are  determined  astronomically 
on  this  principle.  Astronomers  are,  however,  in  the  hmlnt 
of  expressing  the  longitude  of  places  on  the  earth  like  the 


Sfii  itiii' 


RELATION  OF  THE  a^HTU  TO  THE  HEAVENS.  49 


dailj),  we 


,  at  4  o'clock 

k   ■ 

8    0 

048 
16    8 


mWi 


ig  our  civil 
1  that  it  is 
en  the  sun 
:  with  more 
m  under  the 
;he  earth  on 
t  succession, 
pass  in  sue- 
Hence  noon 
in  an  hour, 
The  differ- 
I  it  is  called, 
ir  difference 
16  degrees  of 
M)  on.  Vice 
i  can  deter- 
le  difference 
lifferenoe  <^ 

tronomioaliy 
in  the  halnt 
rth  like  the 


right  ascensions  of  the  heavenly  bodies,  not  in  degrees,  but 
in  hours.  For  instance,  instead  of  saying  that  Washington 
is  77°  3'  west  of  Greenwich,  we  commonly  say  that  it  is  6 
hours  8  minutes  13  seconds  west,  meaning  that  when  it  is 
noon  at  Washington  it  is  5  hours  8  minutes  12  seconds 
after  noon  at  Greenwich.  This  course  is  adopted  to  prevent 
the  trouble  and  confusion  which  might  arise  from  constantly 
having  to  change  hours  into  degrees  and  the  reverse. 

Where  does  the  Day  Change  1— A  question  frequently 
asked  c     .is  connection  is.  Where  does  the  day  change? 
It  is,  we  will  suppose,  Sunday  noon  at  Washington.    That 
noon  travels  all  the  way  round  the  earth,  and  when  it  gets 
back  to  Washington  again  it  is  Monday.    Where  or  when 
did  it  change  from  Sunday  to  Monday?    We  answer, 
wherever  people  choose  to  make  the  change.    Navigators 
make  the  change  occur  in  longitude  180°  from  Greenwich. 
As  this  meridian  lies  in  the  Pacific  Ocean,  and  meets 
scarcely  any  land  through  its  course,  it  is  very  convenient  for 
this  purpose.    If  its  use  were  universal,  the  day  in  question 
would  be  Sunday  to  all  the  inhabitants  east  of  this  line,  and 
Monday  to  every  one  west  of  it.    But  in  practice  there  have 
been  some  deviations.    As  a  general  rule,  on  those  islands 
of  the  Pacific  which  were  settled  by  men  travelling  east  the 
day  would  at  first  be  called  Monday,  even  though  they 
might  cross  the  meridian  of  180°.    Indeed  the  Bussian 
settlers  carried  their  count  into  Alaska,  so  that  when  our 
people  took  possession  of  that  territory  they  found  that 
the  inhabitants  called  the  day  Monday  when  they  them- 
selves called  it  Sunday.    These  deviations  have,  however, 
almost  entirely  disappeared,  and  with  few  exceptions  the 
day  is  changed  by  common  consent  \n  longitude  180°  from 
Greenwich. 


!-T-':,''"J. 


00 


ABTROHOMT. 


DiTKumiATiovi  or  TnximiAL  LoMomrsn. 

Owing  to  the  rotution  of  the  earth*  there  is  no  such  fixed 
correspondence  between  meridiMis  on  the  earth  and  among 
the  stars  as  there  is  between  latitude  on  the  earth  and  de- 
clination in  the  heavens.    The  observer  can  always  deter- 
mine his  latitude  by  finding  the  declination  of  his  zenith, 
but  he  cannot  find  his  longitude  from  the  right  ascension 
of  his  zenith  with  the  same  facility,  because  that  right  as- 
cension is  constantly  changing.    To  determine  the  longi- 
tude of  a  place,  the  element  of  time  as  measured  by  the 
diurnal  motion  of  the  earth  necessarily  comes  in.    Gon- 
sider  the  plane  of  the  meridian  of  a  place  extended  out  to 
the  celestial  sphere  so  as  to  mark  out  on  the  latter  the 
celestial  meridian  of  the  place.    Take  two  such  places, 
Washington  and  S^n  Francisco  for  example;  then  there 
will  be  two  such  celestial  meridians  cutting  the  celes- 
tial sphere  so  as  to  make  an  angle  of  about  forty-fire  de- 
grees with  each  other  in  this  case.    Let  the  obsenrer  imagine 
himself  at  San  Fr&ncisoo.     Then  he  may  conceive  the 
meridian  of  Washington  to  be  visible  on  the  celestial  sphere, 
and  to  extend  from  the  pole  over  toward  his  south-east 
horizon  so  as  to  pass  at  a  distance  of  about  forty-five  degrees 
east  of  his  own  meridian.    It  would  appear  to  him  to  be  at 
rest,  although  really  both  his  own  meridian  and  that  of 
WashLgton  are  moving  in  consequence  of  the  earth's  rota- 
tion.   Apparently  the  stars  in  their  course  will  first  pass 
the  meridian  of  Washington,  and  about  three  hours  later 
will  pass  his  own  meridian.    Now  it  is  evident  that  if  he 
can  determine  the  interval  which  the  star  requires  to  pass 
from  the  meridian  of  Washington  to  that  of  his  own  place, 
he  will  at  pQce  have  the  difference  of  longitude  of  the  two 


BELATION  OF  TUB  EARTH  TO  TUB  HEAVENS,  fil 


BRXTOI. 

no  Buch  fixed 
.h  and  among 
earth  and  de- 
always  deter- 
Df  his  zenith, 
ght  ascension 
hat  right  as- 
ine  the  longi- 
asured  by  the 
aes  in.    Gon* 
tended  out  to 
he  latter  the 
such  places, 
>;  then  there 
ng  the  celes- 
forty-five  de- 
lerver  imagine 
conceive  the 
lestial  sphere, 
liis  south-east 
ty-five  degrees 
9  him  to  be  at 
I  and  that  of 
e  earth's  rota- 
will  first  pass 
3e  hours  later 
int  that  if  he 
iqnires  to  pass 
bis  own  plaoe, 
ide  of  the  two 


places  by  simply  turning  tbe  interval  in  time  into  degrees 
at  the  rate  of  fifteen  degrees  to  each  hour. 


rw.14. 

The  difference  of  longitude  between  any  two  places  de- 
pends  upon  the  angular  distance  of  the  terrestrial  (or  celes- 
tial) meridians  of  these  two  places  and  not  upon  the  motion 
of  the  star  or  sun  which  is  used  to  determine  this  angular 
difference,  and  hence  the  longitude  of  a  place  is  the  same 
whether  expressed  as  the  difference  of  two  sidereal  or  of 
two  solar  times.  The  longitude  of  Washington  west  from 
Greenwich  is  S^  8*°  or  77°,  and  this  is  in  fact  the  ratio  of 
the  angular  distance  of  the  meridian  of  Washington  from 
that  of  Greenwich,  to  24  hours  or  360°.  The  angle  between 
the  two  meridiane  is  ^  of  24  hours,  or  of  a  whole  circumo 
fergnoe, 


■UJ,.-. 


iri 


69 


ASTRONOMT. 


It  iB  thus  plttin  that  tlif  difference  of  longitude  of  any  two 
places  is  the  amne  as  the  difference  of  their  eimultaneoua 
local  times;  and  this  whether  the  local  times  spoken  of 
me  both  sidereal  or  both  solar. 

MxTHOM  Of  DiTiBimnjro  thi  Snrruunoi  of  Lovei- 

TTOI  Of  Two  FLAOII  ok  TBI  lASTH. 

Every  purely  astronomical  method  depends  upon  the 
principle  we  have  just  laid  down. 

It  is  of  vital  importance  to  seamen  to  be  able  to  deter- 
mine  the  longitude  of  their  vessels.  The  voyage  from  Liv- 
erpool to  New  York  is  made  weekly  by  scores  of  steamers, 
and  the  safety  of  the  voyage  depends  upon  the  certainty 
with  which  the  captain  can  mark  the  longitude  and  lati- 
tude of  his  vessel  upon  the  chart. 

The  method  used  by  a  sailor  is  this :  with  a  sextant  (see 
Chapter  III.)  the  local  time  of  the  ship's  position  is  deter- 
mined by  an  observation  of  the  sun.  That  is,  on  a  given 
day  he  can  set  his  watch  so  that  its  hands  point  to  twelve 
hours  when  the  sun  is  on  his  meridian  on  that  day.  He 
carries  a  chronometer  (which  is  merely  a  very  fine  watch) 
whose  hands  point  always  to  Gi-eonwich  time.  Suppose 
that  when  tlie  ship's  time  is  0"  or  noon  the  Greenwich 
time  is  3"  20'".  Evidently  he  is  w'.dt  of  Greenwich  S"  80". 
since  that  is  the  difference  of  the  simultaneoua  local  times, 
and  since  the  Greenwich  time  is  later.  Hence  he  is  some, 
where  on  the  meridian  of  60°  west.  If  he  has  determined 
the  altitude  of  the  pole  or  the  declination  of  his  zenith  in 
any  way,  then  he  has  his  latitude  also.  If  this  ehonld  be 
46°  north,  the  ship  is  in  the  regular  track  between  New 
York  and  Liverpool,  and  he  can  go  on  with  safety. 


RKLATION  OF  TUR  EARTB  TO  THE  IlKAVKNa.  58 


d«  of  any  two 
simultaneout 
68  spoken  of 


SI  Of  Lovex* 

;th. 

ds  upon  the 

able  to  deter- 
age  from  Liv- 
I  of  steamers, 
the  certainty 
tude  and  lati- 

a  sextant  (see 
ition  is  deter- 
B,  on  a  given 
>int  to  twehe 
hat  day.  He 
iry  fine  watch) 
me.  Suppose 
ho  Greenwich 
mwich  9,^  gO", 
ii«  local  times, 
ce  he  is  some^ 
as  determined 
t  his  zenith  in 
this  shonld  be 
between  New 
safety. 


When  the  steamer  Faraday  wm  Iftving  the  dirert  cable  the  got  her 
longitude  cvury  day  by  comparing  hur  ship's  timv  (found  by  oliser- 
ralion  on  Imnrd)  with  the  Qrocnwicli  time  telcgraplicd  iiloug  tlie  cable 
and  raceived  at  the  end  of  it  which  she  liad  on  her  dcclc.  Longitudes 
may  be  determined  in  the  same  way  on  shore. 

From  an  observatory,  as  Wasliington,  the  beats  of  a  cloclc  are  sent 
out  by  telegraph  along  the  lines  of  railway;  at  every  railway  sUtion 
and  telegraph  office  the  telegraph  sounder  tients  the  seconds  of  the 
WaMhington  clock.  Any  one  who  can  set  his  watch  to  tlie  local  time 
of  his  station  and  who  can  compare  it  with  the  signals  of  the  Wash- 
ington clock  (which  are  sent  at  ATashington  noon,  daily  except  Sun- 
day) can  determine  for  liimsolf  the  difference  of  the  simuiluneoua 
local  times  of  Washington  and  of  his  station,  and  thus  his  own  longi- 
tude cast  or  west  from  Washington. 

mTROM  ov  DiTiBMnmro  tki  Latittos  or  a  Plaoi 

OK  TBI  EABTH. 

Latitude  from  Giroumpolar  9t«n.— In  tbo  figure  sup- 
pose Z  to  be  the  zenith  of  the  observer,  UZRN  hM  me- 


ria.is. 


ridian,  P  the  north  pole,  HR  his  horizon.  Suppose  iS^and 
iS'  to  be  the  two  points  where  a  eiroumpolar  star  crosses 
the  meridian^  as  it  mores  around  the  pole  in  its  apparent 


"V  ■-"■- 


wxr 


M'^miikikm,mimimMlm~ 


04 


ABTJiONOMT. 


•■f 


diurnal  orbit.     P  8  =  P  S'  is  the  itar's  north-polar  dii- 
tance,  and  P II  =  <p  =  tl>e  obiorver'g  latitude. 

^±_^  =  ZP  =  00" 


^. 


Therefore 


9=  90° 


ZS^ZS' 


We  can  mcaauro  Z<S  and  iTfi',  the  zenith  diBUnces  of  the 
star  in  the  two  iwsitions,  by  the  meridian  circle  or  by  the 
sextant,  as  will  be  explained  in  the  next  chapter.  Hence 
having  these  zenith  distances  we  have  the  latitude  of  the 

place. 

Latitade  by  the  Meridian  Altitude  of  the  Bon  or  a  Star. 
—In  the  figure  let  Z  be  the  observer's  zenith,  /*  the  pole, 

and  Q  the  intersection  of 
the  celestial  equator  with  the 
meridian //if  i/.  The  alti- 
tude of  the  star  8  is  meas- 
ured when  the  star  is  on  the 
meridian.  It  is  known  to 
be  on  the  meridian  when  wo 
find  its  Hltitudc  lobeamax- 
Fm.  IS.  imum.     From  the  measured 

altitude  of  the  star  8  we  deduce  its  zenith  distance  Z8-Z 
—  90°—  118-    It>  declination  is  taken  from  a  catalogue  of 
stars  if  it  is  a  star,  or  from  the  Nautical  Almanac  if  it  is 
the  sun.    In  either  case  the  declination  C  'Sf  is  known. 
ZQ=QS-\-Z8; 
qt=    6    -\-  H. 

If  the  body  culminates  north  of  the  zenith  at  flf , 
ZQ=Q8'-Z8i 


Ii-pokr  di>* 


RKLATION  OF  TttB  KARTll  TO  WK  IlKAVKNB.  68 

This  is  the  method  uniformly  employed  ut  sea,  where  the 
altitude  of  the  Hun  at  apparent  noon  Ih  daily  measured. 


ances  of  the 
de  or  by  the 
tor.  Hence 
itude  of  the 

in  or  a  Star. 
r  the  pole, 
orsoction  of 
iitor  with  the 
r.     The  alti- 
ir  8  is  meas- 
itur  is  on  the 
is  known  to 
iian  when  we 
I  lobeamax- 
the  measured 
»uce  ZS  =  Z 
,  catalogue  of 
nnnac  if  it  is 
B  known. 


At  8', 


Fasaixazxi  Aim  BmisiAiaTBBf  or  thi  Hiatiwlt 

BODII& 

The  apparent  position  of  a  body  on  the  celestial  sphere 
remains  the  same  as  long  as  the  observer  is  fixed,  as  haa 
been  shown  (see  page  20).  If  the  observer  changes  his 
])1iu«  and  the  star  remains  in  the  same  )M)sition,  the  ap- 


Tm.  17. 

parent  position  of  the  star  will  change.  T<>  show  this  let 
CW  be  the  earth,  C  being  its  centre.  S*  and  8'  are  the 
places  of  two  observers  on  the  surface.  Z"  and  Z'  are 
their  zenith  in  the  celestial  sphere  H'P".  P  is  a-  star. 
8*  will  see  P  in  the  apparent  position  P'.  8"  will  see  P 
in  the  apparent  position  P*.  That  is,  two  different  ob- 
servers see  the  same  object  in  two  different  'apparent 
positions.  If  the  observer  y  moves  along  the  surface 
directly  to  S*,  the  apparent  position  of  P  on  the  celes- 
tial sphere  will  appear  to  move  fr^m  P'  to  P*. 
This  change  is  due  to  the  parallax  of  P. 


feui>jsiiMiaajaaa.'atxx~: 


<        I. 


66 


ASTRONOMT. 


The  parallax  of  a  body  due  to  a  change  in  the  position 
of  the  observer,  is  the  alteration  in  the  apparent  position 
of  the  body  caused  by  that  change. 

If  the  observer  at  S*  could  move  to  the  centre  of  the 
earth  along  the  line  S'C,  the  apparent  position  of  P  wonld 
move  from  P*io  P^  It  the  observer  at  /S*  conld  move 
from  S*  to  C  along  S'C,  the  appannt  position  of  P  would 
move  from  P'  to  P^. 

In  the  triangle  P  S'C  the  following  parts  are  known: 

CP  =  J  =  the  geocentric  distance  of  P, 
CiSf'  =  p'  =  the  radins  of  the  earth  at  S', 

and  the  angle  S'PC  =  P'P  P,  is  the  parallax  of  P. 

For  the  change  of  apparent  position  of  P  from  P'  to  P^ 
is  due  to  the  change  of  the  point  of  observation  from  S*  to 

a 

Similarly  the  angle  S'PC  =  P'PP,  is  the  parallax  of  P 
relative  to  a  change  of  the  observer  fiom  8'  to  C. 

Horixontal  Parallax. — Olearly  the  parallax  of  P  differs 
for  observers  differently  sitnated  on  the  earth,  and  it  is 
necessary  to  take  some  standard  parallax  for  each  observer. 
Such  a  standard  is  the  horizontal  parallax.  Suppose  P 
to  be  in  the  horizon  of  the  observer  S';  then  Z'S'P 
will  be  90°,  as  will  also  the  angle  PS'C.  In  the  triangle 
S'PC  three  parts  will  then  be  known  and  the  horiiontal 
parallax  (the  angle  at  P  when  P  is  in  the  horizon)  can  be 
found.  It  will  be  the  same  for  the  observer  at  5*.  When 
P  is  in  the  horizon  of  S',  Z'S'P  is  a  right  angle,  as  is  also 
PS'C.  CP  and  CS'  are  known  and  thus  the  horizontal 
parallax  of  P  is  determined. 

If  CP,  the  distance  of  P,  increases,  other  things  remain- 
ing the  same,  the  parallax  of  P  will  diminish. 


mtlm 


V     _ 


the  position 
ent  position 

ntre  of  the 
of  P  would 
conid  moTe 
of  P  would 

known: 
tP, 

of  P. 

►m  P'  to  P, 

I  from  8'  to 

arallax  of  P 

C. 

a  P  differa 
b,  and  it  is 
sh  observer. 

Suppose  P 
then  rS^P 
the  triangle 
B  horiiontal 
son)  can  be 

5*.  When 
le,  as  is  also 
le  horisontal 


mgs  remain- 


RBLATtoiT  OP  ma  MAttm  fd  fan  a^Avism.  &t 

The  student  can  prove  this  foi*  himself  by  dwwing  the 
figure  on  the  same  scale  as  here  given,  making  CP  latgen 

The  angles  at  P  (the  parallaxes)  -.vill  become  sitiiillei-  and 
smaller  the  larger  C7P  is  taken.  Hence  the  magnitude  of 
the  pai-allax  of  a  star  or  a  plaudt  depends  upon  its  distance 

from  us. 

Suppose  an  observer  at  the  point  P  looking  at  the  earth's 
radius  S'C.  The  angle  subttmdcd  by  that  semidiameter 
is  the  same  as  the  parallax  of  P.  Hence  we  may  say  that 
the  parallax  of  a  body  with  reference  to  an  observer  on  the 
earth  is  measured  by  the  angle  subtended  by  that  semidi- 
ameter of  the  earth  which  passes  through  the  observer's 

station. 

As  the  point  P  is  carried  further  and  further  away  from 
the  earth,  the  angle  subtended  by  ^C,  for  example,  becomes 
less  and  less.  If  P  were  at  the- distance  of  the  moon,  this 
angle  would  be  about  67';  if  at  the  distance  of  the  sun, 
it  would  be  about  8^'.  S'C  is  roughly  4000  miles;  it 
subtends  an  angle  of  57'  at  the  distance  of  the  moon.  70 
miles  would  subtend  an  angle  of  about  1',  and  3437' 
would  be  about  340,000  miles.  This  is  the  distance  of  the 
moon  from  the  earth.     (See  pages  4,  5.) 

Again,  4000  miles  subtends  an  angle  of  8*.  5  at  the  dis- 
tance of  the  sun.  470.7  miles  would  subtend  an  angle  of 
1',  and  206,264*. 8  would  be  97,000,000  miles,  and  this  is 
about  the  distance  of  the  sun.  By  taking  the  exact  values 
Qf  the  radius  of  the  earth  and  of  the  solar  paralkx,  this  dis- 
tance is  found  to  be  about  93,000,000  miles. 

The  example  shows  the  method  of  calculating  the  sun's 
distance  when  we  have  two  things  accurately  given:  first, 
the  dimensions  of  the  earth;  and  second,  the  parallax  «£ 
the  snn. 

r   * 


tS6 


A6TR0N0MT 


Annual  Parallax. — We  have  seen  that  for  the  moon  the 
parallax  is  about  1°;  for  the  san  it  is  only  8';  for  some  of 
the  more  distant  planets  it  is  considerably  less. 

For  Jupiter  it  is  aboat  2';  for  Saturn  less  than  1';  for 
Neptune  abont  0'.3. 

Let  us  remember  what  this  means.  It  means  that  4000 
miles,  the  earth's  radius,  would  Bubt«nd  at  the  distance  of 
Neptune  an  angle  of  only  A  of  a  single  second  of  arc. 

The  parallax  of  the  moon  is  determined  by  observation, 
and  the  observations  consist  in  measuring  the  angle  which 
the  radius  of  the  earth  would  subtend  if  viewed  from  the 
moon's  centre.  57'  is  an  angle  large  enough  to  be  deter- 
mined quite  accurately  in  this  way.  There  would  be  but  a 
small  per  cent  of  error.  Even  8',  the  sun's  parallax,  can  be 
measured  so  as  to  have  an  error  of  not  more  than  2  or  3 
per  cent. 

But  this  method  will  not  do  to  measure  anything  much 
smaller  than  8'.  The  parallax  of  a  fixed  star,  for  example, 
IS  not  si^sif  part  as  large  as  the  sun's  parallax:  and  this 
is  too  minute  a  quantity  to  be  deduced  by  these  methods. 
We  therefore  use  for  distant  bodies  a  parallax  which  does 
not  depend  on  the  radius  of  the  earth,  but  upon  the  radius 
of  the  earth's  orbit  around  the  sun. 

The  annual  parallax  of  a  body  is  the  angle  subtended  at 
the  body  by  the  radius  of  tJie  earth's  orbit  seen  at  right 
angles. 

For  example,  in  ^ig.  18  suppose  that  Cnow  repi'esents 
the  sun,  around  which  the  earth  8*  moves  in  the  nearly 
circular  orbit  S'S'Jff'.  S'Cia  no  longer  4000  miles  as  in 
the  last  example,  but  it  is  93,000,000  miles.  Suppose  P  to 
be,  again,  a  body  whose  annual  paraUax  is  S'P  C  (suppose 
ing  Pi^O  to  be  a  right  angle). 


\  _ 


he  moon  tbe 
for  some  of 

than  1';  for 

ins  that  4000 

e  distance  of 

1  of  arc. 

observation, 

angle  which 

wed.  from  the 

to  be  deter- 

ould  be  but  a 

rallax,  can  be 

9  than  2  or  3 

lything  much 
for  example, 
ax:  and  this 
ese  methods. 
I  which  does 
on  the  radius 

subtended  at 
seen  at  right 

>w  repi'esentfl 
in  the  nearly 
0  miles  as  in 
Suppose  P  to 
F  C  (suppoB- 


RELATION  OF  THE  EARTH  TO  THE  HEAVENS.  69 

Some  of  the  nearest  fixed  stars  have  an  annual  parallax 
of  nearly  1'.  Hence  the  nearest  of  them  are  not  nearer 
than  206,264  times  93,000,000  miles.  The  greater  number 
of  them  have  a  parallax  of  not  more  than  ^'. 

Hence  their  distances  cannot  be  less  than 

10  X  206,264  X  93,000,000  miles. 

To  the  student  who  has  understood  the  simple  rules  giyen 
on  pages  4  and  5  these  deductions  will  be  plain. 


Fia.  la 

Semidiameten  of  the  Heavenly  Bodies.— The  angular 
semidiameter  of  the  sun  as  seen  from  the  earth  is  961'. 
Hence  its  diameter  is  1922'.  Its  real  diameter  in  miles  is 
therefore  about  880,000,  as  its  distance  is  93,000,000  miles. 

The  angular  semidiameter  of  the  moon  as  seen  from  the 
earth  is  about  15^'.  Hence  its  real  diameter  is  about  2000 
miles,  its  distance  being  about  240,000  miles. 

In  the  same  way,  knowing  the  distance  of  any  planet  and 
measuring  its  angular  semidiameter,  we  can  compute  its 
dimensions  in  miles. 


■Mi 


1 


it  '  I 


1  I 

!'  i 

I!  I 

ii  1 

!•  ! 


i: 


i  :  .i 


CHAPTER  Itt. 

ASTRONOMICAL  INSTRUMENTS. 

General  Aeeoimt — ^In  a  general  way  we  may  divide  the 
instraments  of  astronomy  into  two  claBses,  seeing  instru- 
ments and  meaauring  instruments. 

The  seeing  instruments  are  telescopes;  they  have  for 
their  object  either  to  enable  the  observer  to  see  'foint  objects 
88  comets  or  small  stars,  or  to  enable  him  to  see  brighter 
stars  with  greater  precision  than  he  could  otherwise  do. 
How  they  accomplish  this  we  shall  shortly  explain.  The 
measuring  instruments  are  of  two  classes.  The  first  class 
measures  intervals  of  time.  The  second  measures  angUs. 
A  clock  is  a  familiar  example  of  the  first  class;  a  divided 
circle  of  the  second. 

Let  us  take  these  in  the  order  named. 

The  Sefhusting  Telescope. — The  refracting  telescope  is 
composed  of  two  essential  parts,  the  object-glass  or  objec- 
tive and  the  eye-piece. 

The  object-glass  is  for  the  sole  purpose  of  collecting  the 
rays  of  light  which  emanate  from  the  thing  looked  at,  and 
for  making  an  image  of  this  thing  at  a  point  which  is  called 
the /ocu«  of  the  objective. 

The  eye-piece  has  for  its  sole  object  to  magnify  the  image 
so  that  the  angular  dimensions  of  the  thipg  looked  at  ;will 
appear  greater  when  the  telescope  is  used  than  when  it  is 
not. 


\  _ 


ay  divide  the 
feeing  instra- 

hej  have  for 
I  laint  objects 
>  see  brighter 
otherwise  do. 
ixplain.  The 
rhe  first  class 
asnres  angles, 
ma;  a  divided 


;  telescope  is 
glass  or  objec- 

!olIecting  the 
ooked  at,  and 
rhich  is  called 

tify  the  image 
ooked  at  mil 
tan  when  it  is 


ASTRONOMICAL  iNSTRVMENTa. 

For  example,  in  the  figure  suppose  BI  to 
bo  a  luminous  surface.  Every  iioint  of  it  is 
throwing  off  rays  of  light  in  straight  lines  in 
every  possible  direction.  Let  us  consider  the 
point  /.  The  rays  from  /proceed  m  every 
direction  in  which  we  can  draw  a  straight  line 
through  I.  Suppose  all  such  straight  lines 
drawn.  Let  00'  be  the  objective  of  a  tele- 
scope pointed  towards  BI.  All  the  rays  from 
/  which  fall  on  00'  lie  between  the  lines  10, 
and  I(y.  No  others  can  reach  the  objective, 
and  all  others  which  proceed  from  /  are 
wasted  so  far  as  seeing  /  with  this  particu- 
lar telescope  is  concerned. 

The  action  of  the  convex  lens  0&  is  to 
bend  every  ray  which  passes  through  it  to- 
wards its  axis  BA.  10  is  bent  down  to  OF; 
10'  is  bent  up  to  O'/*;  and  so  for  every 
other  ray  except  the  ray  from  /  through  the 
centre  of  Off  which  is  bent  neither  up  nor 
down,  but  which  goes  straight  on  to  i*  and 
beyond. 

Every  one  of  the  rays  of  light  sent  out  by 
/  between  the  limits  10  and  /O'  finally  passes 
through  1*.  /  is  a  point  of  light,  and  so  is 
r.  The  point  /'  is  the  focus  of  OO*  with 
respect  to  /. 

Sim-rarly  B  sends  out  light  in  every  direc- 
tion. Only  those  rays  which  chance  to  fall 
between  BO  and  BO'  are  useful  for  seeing 
J9^ith  this  particular  ielesoope.  Every  one 
<rf  this  bundle  of  x»]W  comes  to  tk  focus  on  the 


'« 


VMk  n^ 


^If" 


1  "    ('.: 


i    ' 


r__ 


es  ASTRONOMY. 

intersection  of  the  lines  F and  BA .    In  the  same  way 

every  point  of  the  object  BI  has  a  corresponding  image  on 

the  line  F somewhere  between  /'  and  the  axis  BA. 

J' is  the  focal  plane  of  the  objective  with  respect  to 

the  object  BI,  and  the  image  of  BI  lies  in  this  focal  plane. 
The  objective  has  now  done  all  it  can;  it  has  gathered 
every  possible  ray  from  the  object  BI  and  presents  every 
one  of  these  rays  concentrated  in  an  image  of  this  object 
in  the  focal  plane  at  T' 

Notice  two  things:  first,  the  image  is  inverted  with  re- 
spect to  the  object;  I  is  above  B;  the  image  of  /  is  below 

the  image  of' 5;  second,  the  rays  from  B /do  not 

stop  at  /' ,  but  go  on  indefinitely  to  the  left,  always 

diverging  from  the  image. 

The  Bye-piece. — The  eyepiece  is  essentially  a  microscope 
which  is  simply  to  magnify  the  angular  dimensions  of  the 
object  ae  it  is  seen  in  the  telescope;  that  is,  to  magnify  the 
image.  To  see  well  with  a  microscope  it  must  be  close  to 
the  thing  magnified.  It  cannot  be  placed  near  to  BI  in 
general,  for  BI  may  be  a  mile  or  ten  millions  of  miles 
away.  So  the  place  to  put  it  is  near  to  the  image  of  BI,  a 
little  above  the  focal  plane  F in  the  figure. 

The  eye  must  be  placed  a  little  further  above  still, 
at  such  a  position  as  to  see  well  with  the  eye-piece.  That 
is,  close  to  it  Now  fix  an  objective  in  one  end  of  a  tube 
and  an  eye-piece  in  the  other  end  and  you  have  a  refracting 
telescope.  The  more  powerful  the  microscope  used  as  an 
eje-piece  the  higher  the  magnifying  power  of  the  combina- 
tion. We  increase  the  magnifying  power  of  any  telescope 
^  changing  the  eye-piece.  ' 

i  ,?;Th«  Objeetive.— As  a  matter  of  fact  the  objective  is  nra- 
'il%  made  of  two  ghtsses  like  the  figure,  Where  the  arrow 


».  .         .-  .4 


yyiiy 


'wmmm 


L 


ASTRONOMICAL  INSTRUMENTS. 


68 


a  the  Bame  Mray 
ding  image  on 
1  the  axis  BA. 
with  respect  to 
bis  focal  plane. 
;  has  gathered 
presents  every 
of  this  object 

erted  with  re- 
)  of  /  is  below 

/do  not 

;he  left,  always 

y  a  microscope 
tensions  of  the 
to  magnify  the 
ist  be  close  to 

near  to  BI  in 
llions  of  miles 
imnge  of  BI,  a 
igure. 

er  aboye  still, 
e-piece^    That 

end  of  a  tube 
,ye  a  refracting 
>pe  used  as  an 
if  the  combina- 
)f  any  telescope 

bjeotive  is  usn- 
h6re  the  arrow 


shows  the  direction  in  which  the  rays  come  to  it  from  the 
object.     If  wo  use  a  fingle  ob- 
jective we  find  that  the  image  of 
the  object  is  colored ;  that  is,  of 
different  colors  from  its  natural 

tints.    We  find  that  by  using  a  

double  objective  made  of  two  Fw».». 

different  kinds  of  glass  this  can  be  corrected.  This  is  ex- 
plained in  Optics  under  the  head  of  Achromatism  or  Chro- 
matic Aberration. 

Light-gathering  Power.— It  is  not  merely  by  magnifying 
that  the  telescope  assists  the  vision,  but  also  by  increasing 
the  quantity  of  light  which  reaches  the  eye  from  the  object 
at  which  we  look.     Indeed,  should  we  view  an  object 
through  an  instrument  which  magnified  but  did  not  in- 
crease the  amount  of  light  received  by  the  eye,  it  is  evident 
that  the  brilliancy  would  be  diminished  in  proportion  as 
the  surface  of  the  image  was  enlarged,  since  a  constant 
amount  of  light  would  be  spread  over  an  increased  surface; 
and  thus,  unless  the  light  were  very  bright,  the  object  might 
become  so  darkened  as  to  be  less  plainly  seen  than  with  the 
naked  eye.    How  the  telescope  increases  the  quantity  of 
light  will  be  seen  by  considering  that  when  the  unaided 
eye  looks  at  any  object,  the  retina  can  only  receive  so  many 
rays  as  fall  upon  the  pupil  of  the  eye.     By  the  use  of  the 
telescope  it  is  evident  that  as  many  rays  can  be  brought  to 
the  retina  as  fall  on  the  entire  object-glass.    The  pupil  of 
the  human  eye,  in  its  normal  state,  has  a  diameter  of  about 
one  fifth  of  an  inch,  and  by  the  use  of  the  telescope  it  is 
virtually  increased  in  surface  in  the  ratio  of  the  square  of 
the  diameter  of  the  objective  to  the  square  of  one  fifth  of 
m  inchj  that  is,  in  the  r^tio  of  the  sur/act  of  the  objective 


«4 


ABTRONOMT. 


:hrll 


to  the  surface  of  the  pnpil  of  the  eye.  Thus,  with  a  two- 
inch  aperture  to  our  telescope,  the  number  of  rays  collected 
is  one  hundred  times  as  great  as  the  number  collected  with 
the  naked  eye. 

With  a  5-inch  object-glass  the  ratio  ia      820  to  1 

"      10 2,600  to  1 

"  16  ••  "  "  "  6.026  to  1 
"  20  "  "  "  "  10.000  to  1 
"      26    • 16,900  to  1 

When  a  minute  object,  like  a  small  star,  is  viewed,  it  is 
necessary  that  a  certain  number  of  rays  should  fall  on  the 
retina  in  order  that  the  star  may  be  visible  at  all.  It  is 
therefore  plain  that  the  use  of  the  telescope  enables  an 
observer  to  see  much  fainter  stars  than  he  could  detect  wil>> 
the  naked  eye,  and  also  to  see  faint  objects  much  better 
than  bv  unaided  vision  alone.  Thus,  with  a  26-inoh  tele- 
scope  we  may  see  stars  so  minute  that  it  would  require  the 
collective  light  of  many  thousands  to  be  visible  to  the 
unaided  eye. 

Eye-piece. — In  the  skeleton  form  of  telescope  before  de- 
scribed the  eye-piece  as  well  as  the  objective  was  considered 
as  consisting  of  but  a  single  lens.  But  with  such  an  eye- 
piece vision  is  imperfect,  except  in  the  centre  of  the  field, 
from  the  fact  that  the  image  does  not  throw  rays  in  every 
direction,  but  only  in  straight  lines  away  from  the  objec- 
tive. Hence  the  rays  from  near  the  edges  of  the  foeal 
image  fall  on  or  near  the  edge  of  the  eye^piece,  whence 
arises  distortion  of  the  image  formed  on  the  retina,  and  loss 
of  light.  To  remedy  this  difficulty  a  lens  is  inserted  at  or 
very  near  the  place  where  the  focal  image  isformedyforthe 
purpose  of  throwing  the  different  pencils  (tf  rays  whieb 
^inanat^  fromi  ^he  several  parts  of  the  iiDa|;e,  townrcl  V^ 


'Ul 


JM«i 


wm 


ABTRONOmCAL  INSTnUMENTS. 


8,  with  a  two- 
rays  collected 
collected  with 


astol 
OOtol 
25tol 
OOtol 
OOtol 

i  viewed,  it  is 
Id  fall  on  the 
I  at  all.  It  is 
pe  enables  an 
Id  detect  witV 
much  better 
26-inoh  tele- 
Id  reqnire  the 
isible  to  the 

pe  before  de- 
ras  considered 
such  an  eye- 
of  the  field, 
rays  in  every 
>m  the  objec- 
I  of  the  foeal 
piece,  whence 
}tina,  and  loss 
inserted  at  or 
armed,  for  the 
f  rays  whiehf 
e,  townrcl  tlk9 


axis  of  the  telescope,  so  that  they  shall  all  pass  nearly 
through  the  centre  of  the  eye-lens  proper.  These  two 
lenses  are  together  called  the  eye-piece. 

There  are  some  small  differences  of  detail  in  the  con- 
struction of  eye-pieces,  but  the  general  principle  is  the 
same  in  all 

The  figure  showi  an  eye-plec*  <lr»wn  accurately  to  scale.  0/  Is 
one  of  the  converging  pencils  from  the  object-glaai  wliich  forms  one 
point  (/)  of  the  focal  image  la.  This  image  la  viewed  by  the  fiM. 
bjuFofthe  eye-piece  as  if  it  were  a  real  object,  and  tlie  shaded  pencil 
between  J^and  ^shows  the  coune  of  these  rays  after  deviation  by  F. 
If  there  were  no  ^yt-faiu  E,  an  eye  properly  placed  beyond  1"  would 
see  an  image  at  i'«'.  The  eye-lens  E  receives  the  pencil  of  rays,  and 
deviates  it  to  tlie  observer's  eye  placed  at  such  a  point  that  the  whole 
incident  pencil  will  pass  through  the  pupil  and  foil  on  the  retina,  and 
thus  be  eflectlw.    As  we  saw  in  the  figure  of  the  refracting  telescope, 


m.n. 


every  point  of  the  object  produces  a  pencil  similar  to  01,  and  the 
whole  surfaces  of  the  lenses  FmA  J?  are  covered  with  rays.  All  of 
these  pencils  passing  through  the  pupil  go  to  make  up  the  retinal 
image.  This  image  Is  referred  by  the  mind  to  the  distance  of  distinct 
vision  (about  ten  inches),  and  the  lmage\4/"  represents  the  dimen- 
sion of  the  final  Image  relaUve  to  the  inMjje  al  as  formed  by  the  ob^ 

Jectlve,  and  ~  is  evidently  the  magnifying  power  of  t»iis  pwliculsf 

^yepto<»  used  lu  Qp»bl|i8t|PB  ^Itfe  this  partic«lf r  objective, 


■  ijUUI>t<*^'' 


Rl 


iii  p 

I   '    « I  ill 
I    .     '  '5  I, 


M 


ASTItOyOMY. 


XtflaetiBf  TaltMopM.— As  wo  hnvo  seen,  one  essential  part  of  a 
refracting  tvlescHpe  is  the  objective,  wliicli  brings  all  the  incident  rays 
from  an  object  to  one  focus,  formihg  there  an  image  of  Hint  object. 
In  reflecting  telescopes  (retlectont)  the  objective  is  a  mirror  of  specu- 
lum niolal  or  silvered  gloss  ground  to  lliu  Hlinpe  of  a  paraboloid.  The 
figure  shows  the  action  of  such  a  mirror  on  a  bundle  of  parallel  rayh, 
wliich,  after  impinging  on  it,  are  brought  by  reflection  to  one  focus 
F.  The  image  formed  at  tliis  focus  may  be  viewed  with  an  eye- 
piece, aa  in  the  case  of  the  refracting  telescope. 

The  eyepieces  used  with  such  a  mirror  are  of  tlie  kind  already 
described.    In  the  figure  the  eye-piece  would  have  to  be  placed  to 


.vni 


Tta.t». 


tbe  right  of  the  point  F,  and  the  observer's  head  would  thus  interfere 
with  the  incident  liglit.  Various  devices  have  been  proposed  to  rem- 
edy this  inconvenience,  of  which  the  most  simple  is  to  interpose  a 
email  plane  mirror,  which  is  inclined  45°  to  the  line  AC,  just  to  the 
left  of  F.  TIds  minor  will  reflect  the  rays  which  are  moving  towards 
the  focus  Fdova  (in  the  figure)  to  another  focus  outside  of  the  main 
beam  of  rays.  At  this  second  focus  the  eye-piece  is  placed  and  the 
observer  looks  into  it  in  a  direction  perpendicular  to  AC. 

The  Teleicopr  in  MeMturement. — A  telescope  is  generally 
thoaght  of  only  as  an  instrument  to  assist  tbe  eye  by  its 
magnifying  and  ligbt-gatbering  power  in  tbe  manner  we 
have  described.  But  it  bas  a  very  important  additional 
function  in  astronomical  measurements  by  enabling  the 
astronomer  to  point  at  a  celeHtial  object  with  a  certainty 
and  accuracy  otherwise  unattainable.  This  function  of 
the  telescope  was  not  recognized  for  mo^e  than  htilf  a  c^u- 


m 


1 


ASTRONOMICAL  INSTRUMENm 


91 


ntinl  part  of  a 
lie  incident  rays 
I  of  Hint  object, 
nirrurof  specu- 
rnlioloiil.  Tlio 
if  parallel  rayh, 
n  to  one  focus 
d  with  an  cyc- 
le kind  already 
0  be  placed  to 


d  thus  interfere 
reposed  to  rem- 
to  interpose  a 
AC,  just  U)  the 
noving  towards 
lide  of  the  main 
placed  and  the 
AC. 

e  is  generally 
bhe  eye  by  its 
16  manner  wo 
nt  additional 
enabling  the 
;h  a  certainty 
\  function  of 
an  h^lf  a  c^vr 


tury  after  its  invention,  and  after  a  long  and  rather  aori' 
monious  contest  between  two  schools  of  astronomers. 
Until  the  middle  of  the  seventeenth  century,  when  an 
tistronomer  wished  to  determine  the  altitude  of  a  celestial 
object,  or  to  measure  the  angular  distance  between  two 
stars,  he  was  obliged  to  point  his  sextant  or  other  meas- 
uring instrument  at  the  object  by  means  of  "pinnules." 
These  served  the  same  purpose  as  the  sights  on  a  rifle.  In 
using  them,  however,  a  difficulty  arose.  It  was  impossible 
foi  I  he  observer  to  have  distinct  vision  both  of  the  object 
and  of  the  pinnules  at  the  same  time,  because  when  the 
eye  was  focused  on  either  pinnule,  or  on  the  object,  it  waa 
necessarily  out  of  focus  for  the  others.  The  only  way  to 
diminish  this  difficulty  was  to  lengthen  the  arm  on  which 
the  pinnules  were  fastened  so  that  the  latter  should  be  ai 
far  apart  as  possible.  Thus  Tycho  Brahe,  before  the 
year  1600,  had  measuring  instruments  ver/  much  larger 
than  any  in  use  at  the  present  time.  But  this  plan  only 
diminished  the  difficulty  and  could  not  entirely  obviate  it, 
because  to  be  manageable  the  instrument  must  not  be  very 
large. 

About  1670  the  English  and  French  astronomers  found 
that  by  simply  inserting  fine  threads  or  wires  exactly  in 
the  focus  of  the  object-glass,  and  then  pointing  it  at  the 
object,  the  image  of  that  object  formed  in  the  focus  could 
be  made  to  coincide  with  the  threads,  so  that  the  observer 
could  see  the  two  exactly  superimposed  upon  each  other. 
When  thus  brought  into  coincidence,  it  was  obvious  that 
the  point  of  the  object  on  which  the  wires  were  set  was  in 
a  straight  line  passing  through  the  wires,  and  through  the 
centre  of  the  object-glass.  So  exactly  could  such  a  point- 
ing be  made,  that  if  the  telescope  did  not  magnify  at  all 


Ofi 


ASrnONOMT. 


(tho  oye-piecij  and  objcct-gliisa  being  of  oqiiul  focal  length), 
a  Tory  important  lidvance  would  still  be  made  in  the  ac- 
curacy of  astronomical  mciisurcmcnts.  This  line,  passing 
centrally  through  tho  telescope,  we  call  the  line  of  colli- 
tnution  of  the  telescope,  A  B  in  Fig.  19.  If  wo  have  any 
way  of  determining  it,  it  is  as  if  we  had  an  indefinitely  long 
pencil  extended  from  the  earth  to  the  sky.  If  the  observer 
rimply  sets  his  telescope  in  a  fixed  position,  looks  through 
it  and  notices  what  stars  pass  along  the  threads  in  tho  eye- 
piece, he  knows  that  all  those  stars  lie  in  the  axis  of  col> 
limation  of  his  telescope  at  that  instant 

By  the  diurnal  motion  a  pencil-mark,  as  it  were,  is  thui 
drawn  on  the  surface  of  the  celestial  sphere  among  th« 
stars,  and  th6  direction  of  this  pencil-mark  can  be  deter- 
mined with  far  greater  precision  by  the  telescope  than  with 
the  naked  eye. 


CHBOHOMITIBB  AlTD  OlOOXft 

We  have  seen  that  it  is  important  for  various  pnrposeB 
that  an  observer  should  be  able  to  determine  his  local  time 
(see  page  62).  This  local  time  is  determined  most  accu- 
rately by  observing  the  transits  of  stars  over  the  celestial 
meridian  of  the  place  where  the  observer  is.  In  order  to 
determine  the  moment  of  transit  with  all  required  accuracy, 
it  is  necessary  that  the  time-pieces  by  which  it  is  measured 
shall  go  with  the  greatest  possible  precision.  There  is  no 
great  difficulty  in  making  astronomical  measures  to  a  sec- 
ond of  arc,  and  a  star,  by  its  diarnal  motion,  posses  over 
this  space  in  one  fifteenth  of  a  second  of  time  (see  page 
44).  It  is  therefore  desirable  that  the  astronomical  clock 
shall  not  v^ry  from  a  uniform  rate  more  than  a  few 


ASTBOyOMICAL  JNSTltUMKNTS. 


c»cal  length), 
B  in  the  no- 
line,  paMing 
line  of  colli- 
tvo  have  any 
Bfinitely  long 
the  obserrer 
oks  through 
Is  in  the  eye- 
axis  of  col« 

were,  is  thus 

among  th« 

!an  be  deter- 

pe  than  with 


f)U8  purposes 
lis  local  time 
L  most  acctt- 

the  celestial 

In  order  to 
red  accuracy, 
>  is  measured 

There  is  no 
[ires  to  a  seo- 
I,  passes  oyer 
me  (see  page 
omical  clock 

than  a  few 


hundredths  of  a  sooond  in  the  course  of  a  day.  It  is 
not,  however,  necessary  that  it  should  always  be  perfectly 
correct;  it  may  go  too  fast  or  too  slow  without  detracting 
from  its  character  for  accuracy,  if  the  intervals  of  time 
which  it  tells  off — hours,  minutes,  or  seounds — uro  always 
of  exactly  the  same  length,  or,  in  other  words,  if  it  gains 
or  loses  exactly  the  same  amount  every  hour  and  every 
day. 

The  time-pieces  used  in  astronomical  observation  are  the 
ohronometor  and  the  clock. 

The  chronometer  is  merely  a  very  perfect  watch  with 
a  balance-wheel  so  constructed  that  changes  of  tempera- 
ture have  the  least  possible  effect  upon  the  time  of  its 
oscillation.  Such  a  balance  is  called  a  compensation  bal- 
ance. 

The  ordinary  house-clock  goes  faster  in  cold  than  in 
warm  weather,  because  the  pendulum-rod  shortens  under 
the  influence  of  cold.  This  effect  is  such  that  the  clock 
will  gain  about  one  second  a  day  for  every  fait  cf  3°  Cent. 
(5°.4  Fahr.)  in  the  temperature,  supposing  the  pendulum- 
rod  to  be  of  iron.  Such  changes  of  rate  would  be  entirely 
inadmissible  in  a  dock  used  for  astronomical  purposes. 
The  astronomical  clock  is  therefore  provided  with  a  com- 
peneation  pendulum,  by  which  the  disturbing  effects  of 
changes  of  temperature  lire  avoided. 

The  correetion  of  a  clock  is  the  quantity  which  it  is  necesaary  to 
add  to  the  indications  of  tlie  hands  to  obtain  th«  true  time.  Thus  if 
the  correction  of  a  sidereal  cloclc  is  +  1"  Kf-OT  and  the  hands  point 
to  810  18"  14'.80,  tlie  correct  sidereal  time  is  21^  14"  24*.57. 

The  rate  of  a  chnik  is  the  daily  change  of  its  correction;  i.e.,  what 
it  gains  or  loses  daily. 


wfK 


n 


:^i    ," 


ill  ill 


70 


A8TB0N0MT. 


The  Tsaksit  Instbvmeht. 


The  Transit  Instrument  is  used  to  observe  the  trw.sits 
of  stars  over  the  celestial  meridian.    The  times  of  these 


E>^H 


Fio.  30. 


transits  are  noted  by  the  sidereal  clock,  which  is  an  indis- 
pensable adjunct  of  the  transit  instrument. 


■  ..m»i  w 


ASmONOMIOAL  INSTRUMENTS. 


71 


the  traR.sits 
es  of  these 


N 


is  an  indis- 


It  consists  essentially  of  a  telescope  TT  mounted  on  an  axis  VV 
at  right  angles  to  it.  Tlie  ends  of  this  axis  terminate  in  accurately 
'cy\indrical  pivots  which  rest  in  metallic  bearings  VY  which  are 
shaped  like  the  letter  Y,  and  hence  called  the  Y's. 

These  are  fastened  to  two  pillars  of  stone,  brick,  or  iron.  Two 
counterpoises  WIT  are  connected  with  the  axis  as  in  the  plate,  so  as 
to  take  a  large  portion  of  the  weight  of  the  axis  and  telescope  from 
the  Y's,  and  thus  to  diminish  the  friction  upon  these  and  to  render 
the  rotation  about  FFraore  easy  and  regular.  In  the  ordinary  use 
of  the  transit,  the  line  F  F  is  placed  accurately  level  and  also  perpen- 
dicular to  the  meridian,  or  in  the  east  and  west  line.  To  effect  this 
"adjustment"  there  are  two  sets  of  adjusting  screws,  by  which  the 
ends  of  F  F  in  the  Y's  may  be  moved  either  up  and  down,  or  north 
and  south.  The  plate  gives  the  form  of  transit  used  in  permanent 
observatories,  and  shows  the  observing  chair  G,  the  reversing  carriage 
B,  and  the  level  L.  The  arms  of  the  latter  have  Y's,  which  can  be 
placed  over  the  pivots  VV. 

The  Um  of  eoUimation  of  the  transit  telescope  is  the  line  drawn 
through  the  centre  of  the  objective  perpendicular  to  the  rotation 
axit  VV. 

The  retiele  is  a  network  of  fine  spider-lines  placed  in  the  focus  of 
the  objective. 

In  Fig.  24  the  circle  represents  the  field  of  view  of  a  transit  as  seen 
through  the  eye-piece.  The  seven  vertical 
lines,  I,  II.  Ill,  IV,  V,  VI,  VII,  are  seven  ! 
fine  spider-lines  tightly  stretched  across  a 
hole  in  a  metal  plate,  and  so  adjusted  a* 
to  be  perpendicular  to  the  direction  of  a  | 
star's  apparent  diurnal  motion.  The  hori- 
zontal wires,  guide-wira,  a  and  b,  mark  the  I 
centre  of  the  field.  The  field  is  illuminated 
at  night  by  a  lamp  at  the  end  of  the  axis 
which  shines  through  the  hollow  interior  of 
the  latter,  and  causes  the  field  to  appear 
bright.  "The  wires  are  dark  against  a  bright 
ground.  The  line  of  right  is  a  line  joining  the  centre  of  the  objective 
and  the  central  one,  IV,  of  the  seven  vertical  wires. 

The .  whole  transit  is  in  adjustment  when,  first,  the  axis  F  F  is 
lioriiontal;  second,  when  it  lies  east  and  west;  and  third,  when  the 
line  of  sight  and  the  line  of  eoUimation  coincide.  When  these  condi- 
tions are  fulfilled  the  line  of  sight  intersects  the  celestial  sphere  in  the 
meridian  of  the  place,  and  when  TT  \a  rotated  about  F  F  the  line  of 
right  marks  out.  the  celestial  meridian  of  the  place  on  the  splMre. 


Ro.  Mk 


IW 


72 


ASTRONOMY. 


•*' 


The  clock  etandB  near  the  transit  instrument.  The  times 
when  a  star  passes  the  wires  I-VII  are  noted.  The  average 
of  these  is  the  time  when  the  star  was  on  the  middle  thread, 
or,  what  is  the  same  thing,  on  the  celestial  mendian.  At 
that  instant  its  hour-angle  is  zero.     (See  page  89.) 

The  sidereal  time  at  that  instant  is  the  hour-angle  of  the 
vernal  equinox  (see  page  44).  This  is  measured  from  the 
meridian  towards  the  west.  The  right  ascension  of  the 
star  which  is  observed  is  the  same  quantity,  measured  from 
the  vernal  equinox  towards  the  cast.  As  the  star  is  on 
the  meridian,  the  two  are  equal.  Suppose  we  know  the 
right  ascension  of  the  star  and  that  it  is  a.  Suppose  the 
clock  time  of  transit  is  T.  It  should  have  been  a  if  the 
clock  were  correct.  The  correction  of  the  clock  at  this 
instant  is  thus  a  —  T. 

This  is  the  use  we  make  of  stars  of  known  right  ascen- 
sions. By  observing  any  one  of  them  we  can  get  a  value  of 
the  clock  correction. 

Suppose  the  dock  to  be  correct,  and  suppose  we  note  that 
a  star  whose  right  ascension  is  unknown  is  on  the  wire  IV 
at  the  tiuie  a'  by  the  clock,  a'  is  then  the  right  ascension 
of  that  star.  In  this  way  the  positions  of  stars,  or  of  the 
snn  and  planets  (in  right  ascension  only),  are  determined. 

Vhb  ¥Ki»nTAw  CntoLS. 

The  meridian  circle  is  a  combination  of  the  transit  in- 
strument with  a  graduated  circle  fastened  to  its  axis  and 
moving  with  it.  A  meridian  circle  is  shown  in  Fig.  36. 
It  has  two  oirclee  finely  divided  on  their  sides.  The  grad- 
uation of  each  circle  is  viewed  by  four  microscopes.  The 
microscopes  are  90°  apart.  The  cat  shows  also  the  hntg- 
ing  leva  by  which  the  en-or  of  level  of  the  ws  is  found. 


ASTRONOMICAL  INSTRUMENTS. 


73 


The  times 
The  average 
Idle  thread, 
Tidian.  At 
39.) 

angle  of  ihe 
3d  from  the 
ision  of  the 
osnred  from 
I  star  is  on 
e  know  the 
Suppose  the 
!en  a  if  the 
lock  at  this 

right  ascen- 
ii  a  value  of 

^e  note  that 
the  wire  IV 
lit  ascension 
*8,  or  of  the 
etmmined. 


» transit  in- 
its  axis  and 
m  Fig.  S6. 
The  gnid. 
ciopes.  The 
o  theiuuig- 
is  found. 


The  instrument  can  be  used  as  a  transit  to  determine 
right  ascensions,  as  before  described.  It  can  be  also  used 
to  measure  declinations  in  the  following  way  :  If  the 
telescope  is  pointed  to  the  nadir,  a  certain  division  of 


I 


tho  .  iTcles,  J»8  N,  is  under  the  first  microscope..  "We  can 
irj*ke  Ihu  nadir  a  Visible  point  by  placing  a  hmm  of  quick- 
silver below  the  telescope  and  locking  in  it  through  the  tel- 
escope,    v^e  shall  see  tbe  wires  of  the  reticle  anr!  ,.lso  their 


74 


ABTBONOMT. 


;  i 


t  =!  n  f 


reflected  images  in  the  quicksilver.  When  these  coincide, 
the  telescope  points  to  the  nadir.  If  it  is  then  pointed  to 
the  pole,  the  reading  will  change  by  the  angular  distance 
between  the  nadir  and  the  pole,  or  by  90°  +  q>,  ^  being  the 
latitude  of  the  place  (supposed  to  be  known).  The  polar 
reading  P  of  the  circle  is  thus  known  when  the  nadir 
reading  N\&  found.  If  the  telescope  is  then  pointed  to 
various  stars  of  unknotvn  polar  distances,  p',  p",  p'",  etc., 
as  they  successively  cross  the  meridian,  and  if  the  circle 
readings  for  these  stars  are  P',  P",  P'",  etc.,  it  follows 
that  p'^P'—P;  p"  =  P"_P;  p'"  =  P'"  —  p.,  etc. 

Thus  !:he  meridian  circle  serves  to  determine  by  observa- 
tion both  co-ordinates  of  the  apparent  position  of  a  body. 

Tee  Eqvatobial. 

An  equatorial  telescope  is  one  mounted  in  such  a  way  that 
a  star  may  be  followed  through  its  diurnal  orbit  by  turning 
the  telescope  about  one  axis  only.  The  equatorial  mount- 
ing consists  essentially  of  a  pair  of  axes  at  right  angles 
to  each  other.  One  of  these  SN  (the  polar  axis)  is  direct- 
ed toward  the  elevated  polo  of  the  heavens,  and  it  there- 
fore makes  an  angle  with  the  horizon  equal  to  the  latitude 
of  the  place  (p.  31).  This  axis  can  be  turned  about  its  own 
axial  line.  On  one  extremity  it  carries  another  axis  L  D 
(the  declination  axis),  which  is  fixed  at  right  angles  to  it, 
but  which  can  again  be  rotated  about  its  axial  line. 

To  this  last  axis  a  telescope  is  attached,  which  may  either 
be  a  reflector  or  a  refractor.  It  is  plain  that  such  a  tele- 
scope may  be  directed  to  any  poir  f  the  heavens;  for  we 
can  rotate  the  declination  axis  until  the  telescope  points  to 
any  given  polar  distance  or  declination.  Then,  keeping 
the  telescope  fixed  in  respect  to  the  declination  axis,  we  can 


lese  coincide, 
in  pointed  to 
ular  distance 
,  qt  being  the 
The  polar 
m  the  nadir 
n  pointed  to 
>",  p'",  etc., 
if  the  circle 
c,  it  follows 
-  P;  etc. 
B  by  observa- 
of  a  body. 


ih  a  way  that 
t  by  turning 
}rial  mount- 
right  angles 
•is)  is  direct- 
nd  it  there- 

the  latitude 
bout  its  own 
er  axis  LD 
angles  to  it, 
line. 
1  may  either 

such  a  tele- 
rens;  for  we 
pe  points  to 
len,  keeping 
axis,  we  can 


ASTRONOMICAL  INSTllUMENTS. 


rm.K. 


76 


ASTBONOMT. 


%  1  t 


rotate  the  whole  instrument  as  one  mass  about  the  polar 
axis  until  the  telescope  points  to  any  portion  of  the  parallel 
of  declination  deOned  by  the  given  right  ascension  or  hour- 
angle.  Fig.  26  is  an  equatorial  of  six-inch  aperture  which 
can  be  moved  from  place  to  place. 

If  we  point  such  a  telescope  to  a  star  when  it  is  rising  (doing  this 
by  rotating  tlie  telescope  first  about  its  declination  axis  and  then 
about  tlie  polar  axi»),  and  fix  the  telescope  in  tliis  position,  we  can, 
by  simply  rotating  tlie  whole  apparatus  on  the  polar  axis,  cause  the 
telescope  to  truce  out  on  the  celestial  sphere  the  apparent  diurnal 
path  which  this  star  will  appear  to  follow  from  rising  to  setting.  In 
such  telescopes  a  driving-clock  is  so  arranged  that  it  can  turn  tho 
telescope  round  the  polar  axis  at  the  same  rate  at  which  the  earth  it- 
self turns  about  i'  ■  own  axis  of  rotation,  but  in  a  contrary  direction. 
Hence  such  a  telescope  once  pointed  at  a  star  will  continue  to  point 
at  it  as  long  as  the  driving-clock  is  in  operation,  thus  enabling  the 
astronomer  to  make  such  an  examination  or  obserration  of  it  as  is 
required. 

TBI  SiZTAn. 

The  sextant  is  a  portab  e  instmment  by  which  the  aUituda  at 
celestial  bodies  or  the  angular  4iHanu*  between  them  may  be 
measured.  It  is  used  chiefly  by  navigators  for  determining  the  lati- 
tude and  the  local  time  of  the  position  of  the  ship.  Knowing  the 
local  time,  and  comparing  it  with  a  chronometer  regulated  on  Green- 
wich time,  the  longitude  become*  known  and  the  ship's  place  is 
fixed.    (See  page  53.) 

It  consists  of  an  arc  of  a  divided  circle  usually  60°  in  extent, 
whence  the  name.  This  arc  is  in  fact  divided  into  120  equal  parts, 
each  marked  as  a  degree,  and  theae  are  again  divided  into  smaller 
•paces,  so  that  by  means  of  the  vernier  at  the  end  of  the  index-arm 
M8  an  arc  of  10"  (usually)  may  be  read. 

The  index-arm  M8  carries  the  index-^ii  M,  which  is  a  silvered 
plane  mirror  set  perpendicular  to  the  plane  of  the  divided  arc.  The 
horitonrglau  m  u  also  a  plane  mirror  fixed  perpendicular  to  the  plane 
of  the  divided  cirole. 

Thi8  last  glass  is  fiaad  4a  poalUmi.  -tnAle  the  first  revolves  with  the 
index-arm.  Tlie  horison-^asi  Is  divided  into  two  parts,  of  which 
the  lower  one  is  silvered,  Un  upper  half  being  transparent.  JT  is  a 
telescope  of  low  power  pointed  toward  the  horizon. glass.    By  it  any 


^  * 


}ut  the  polar 
if  the  parallel 
ision  or  hour- 
[)erture  which 


Ising  (doing  this 
I  axis  and  then 
)8ition,  we  can, 

axis,  cause  tlie 
pparent  diurnal 
',  to  setting.    In 

it  can  turn  tho 
ich  the  earth  it- 
iti-ary  direction. 
)ntinue  to  point 
tifl  enabling  the 
ttion  of  it  as  is 


the  aUttudet  of 
them  may  be 

mining  the  lati- 
Knowing  the 

ilated  on  Oreen- 
ship's  place  is 

'  00°  in  extent, 
20  equal  parts, 
!d  into  smaller 
'.  the  index-arm 

ch  is  a  silvered 
Ided  are.  The 
lar  to  the  plane 

solves  with  the 
iart8,  of  which 
Min;nt.  J7  is  a 
188.    By  it  any 


ASTRONOMICAL  INSTRUMENTS. 


n 


object  to  which  it  is  directly  pointed  can  be  seen  through  the  untOterei 
half  of  the  liorizon -glass.  Any  olher  object  in  Mieume  plane  can  be 
brought  into  the  same  field  by  rotatiag  the  index-arm  (and  tlie  index- 
glass  with  it),  so  thai  •  bewn  of  liglit  from  this  second  object  shall 
ilrfhe  tfn  Mex-glass  at  the  proper  angle,  there  to  be  reflected  to  the 
horizon-glass,  and  again  reflected  down  the  telescope  E.  Tlius  the 
images  of  any  two  objects  in  the  plane  of  the  sextant  miiy  be  brought 
together  in  the  telescope  by  viewing  one  directly  au'  .he  other  by 
reflection. 


Wm>  ST 


This  imtniment  is  need  daily  at  sea  to  determine  the 
ship's  position  by  measnring  the  altitude  of  the  sun.  This 
is  done  by  pointing  the  telescope,  EB,  to  the  ma-horison, 
H  in  the  figure,  which  appears  like  a  line  in  the  field  of  the 
telescope,  and  by  moving  the  index-arm  till  the  image  of 


78 


ASmONOMT. 


'Si  H 


the  sun,  B,  coincides  with  the  horizon.  The  arc  read  from 
the  sextant  at  this  time  is  the  sun's  altitude.  From  the 
altitude  of  the  sun  on  the  meridian  the  ship's  latitude  is 
known  (see  page  52).    From  its  altitude  at  another  hour 


I    ! 


the  local  time  can  be  computed.  The  difference  between 
the  local  time  and  the  Greenwich  time,  as  shown  by  the 
ship's  chronometer,  gives  the  ship's  longitude.  By  means 
of  this  simple  instrument  the  place  of  a  vessel  can  be  found 
witnin  a  mile  or  so. 

The  above  are  the  instruments  of  astronomy  which  best 
illustrate  the  principles  of  astronomical  observations. 

Practical  Astronomy  is  the  science  which  teaches  the 
theory  of  these  instruments  and  of  their  application  to  ob> 
Bervation,  and  it  includes  the  art  of  so  combining  the 
observations  and  so  using  the  appliances  as  to  get  the  best 
results. 


%k 


ASmONOMWAL  EPIIEMERIS. 


79 


trc  read  from 
I.  From  the 
p's  latitude  is 
another  hour 


snce  between 

hown  by  the 

By  means 

can  be  found 


jr  which  best 
ations. 
teaches  the 
cation  to  ob« 
nbining  the 
get  the  best 


The  Abtbohomicai  Efeemzsis,  ob  Katttioai  Almanao. 

The  Ailronomieal  Eplieintrii,  or,  as  it  in  more  commonly  called, 
the  Nautical  Almanac,  is  u  work  iu  wliicli  celestial  phenomena  and 
the  positions  of  the  heavenly  Imdies  uro  computed  in  advance. 

The  usefulness  of  such  a  work,  especially  to  the  navigator,  de- 
pends upon  its  regular  oppearauce  on  a  uniform  plan  and  upon  the 
fulness  and  accuracy  of  its  da\a;  it  was  therefore  necessary  that  its 
Jssue  should  bo  taken  up  as  a  government  work.  An  astronomical 
epiieineris  or  nautical  almanac  is  now  published  annually  by  each  of 
the  governments  of  Germany,  Spain,  Portugal,  France,  Great  Britain, 
and  the  United  States.  Tliey  are  printed  three  years  or  more  be- 
forehand, in  order  that  navigators  going  on  long  voyages  may  supply 
themselves  in  advance. 

The  Ephemeris  furnishes  the  fundamental  data  from  which  all  our 
household  almanacs  are  calculated. 

The  principal  quantities  given  in  the  American  Ephemeris  for 
each  year  are  as  follows: 

The  positions  (R.  A.  and  8)  of  the  sun  and  the  principal  large 
planets  for  Greenwich  noon  of  every  day  in  each  year. 

The  right  ascension  and  declination  of  the  moon's  centre  for  every 
Greenwich  hour  in  the  year. 

The  distance  of  the  moon  from  certain  bright  stars  and  planets  for 
every  third  Greenwich  hour  of  the  year. 

The  right  ascensions  and  declinations  of  upward  of  two  hundred 
of  the  brighter  fixed  stars,  corrected  for  precession,  nutation,  and 
aberration,  for  every  ten  days. 

The  positions  of  the  principal  planets  at  every  visible  transit  over 
the  meridian  of  Washington. 

Complete  elements  of  all  the  eclipses  of  the  sun  and  moon,  v»lth 
maps  sliowing  the  passage  of  the  moon's  shadow  or  penumbra  over 
those  regions  of  the  earth  where  the  eclipses  will  be  visible,  and 
tables  whereby  the  phases  of  the  eclipses  can  be  accurately  computed 
for  any  place. 

Tables  for  predicting  the  occultations  of  stars  by  the  moon. 

Eclipses  of  Jupiter't  satellites  and  miscellaneous  phenomena. 

Catalogues  of  Stars.— Of  the  same  general  nature  with  the  Ephe- 
meris are  catalogues  of  the  fixed  stars.  The  object  of  such  a  cata- 
logue is  to  give  tlie  right  ascension  and  declination  of  a  number  of 
stars  for  some  epoch,  the  beginning  of  the  year  1875  for  instance, 
with  the  data  by  which  the  position  of  each  star  can  be  found  at  any 
other  epoch. 


JiWI 

ffff*l 

:  ' .  i 


80 


ASTRONOMr. 


•    'If 


To  give  tlio  student  a  still  further  idea  of  tlic  Ephemtm,  we  preseut 
a  stniill  portion  of  uue  of  iti  pages  for  the  year  1882: 

Febhvabt,  1882— at  Oreknwicii  Mean  Noojt, 


week.  ffS 


The  Bpn's 


i  '; 


Wed. 
Thur. 
FriU. 

8»t 
Bun. 
Mod. 

Tuea, 
Wed. 
Tkur. 

Frid. 

Sat. 

Bun. 

Mod. 
Tues. 
Wed. 

Thur. 
Frid. 
Bat. 


16.8410.141 
19.8810.107 

»1.M  10.078 
28  .3.S  10.040 
«1  80   88.88  lO.OOT 


Apparent 

right 
aaoenHion. 


Diff. 
fori 
hour. 


a. 
18.0110.178  817 


Apparent 
declination. 


31  84  88.68  9.974 
81  88  88.60  9.941 
81  88  80.79  9.909 


81  86  18.81 

81  40  14.88 

81  44  10.80 

81  48  5.98 

81  68  0.43 

81  S5  M.16 

31  89  47.17 

88  8  89.47 

83  7  81.07 


9.87r 
9.816 
9.81.') 

0.784 
9.7S8 
9.788 

9.698 
9.661 
9.685 


16 
16 

16 
15 
16 


3 

45 
87 

9 
51 
83 


33.4 

5.4 

80.9 

89.3 

80.8 

6.1 


15  14  35.4 

14  55  39.1 

14  86  17.7 

14  16  51.6 

18  57  11.8 

18  87  16.9 

18  17  9.1 

18  56  48  8 

18  86  14.9 

13  IS  89.8 

11  54  88.1 

11  88  88.6 


Diff. 
fori 
hour. 


+43.81 
48.67 
44.80 

+44.99 
45.69 
46.86 

+47.08 
47.66 
48.88 

48.88 
49.4' 
50.08 


Equation 
of  time 
to  be 
subtracted 
from 
mean 
time. 


M. 

IS 
18 
14 

14 
14 
14 


B. 

51.84 

58.58 

5.01 

10.61 
16.41 
19.40 


14  88.60 

14  36.01 

14  86.65 

14  37.51 

14  37.68 

14  86.99 


+50.80  14  85.68 
51.18  14  98.53 
51.66    14    80.70 


+88.14 
53.68 
68.07 


14  17.15 
14  18.90 
14     7.M 


0.818 
0.884 
0.850 

0.916 
0.188 
0. 


H.  M.    s. 

30  46  81.70 

39  80  18.86 

30  54  14.81 


18031 


0.117 
0.084 
0.063 

0.030 
0.011 
0.049 

0.078 
0.104 
0.1S4 


Sidereal 

time 
or  riftht 
aaoenaion 

of 
meanaun. 


30  88  11.97 
81  9  7.93 
•    4.48 


91  10    1.08 

91  18  B7.80 

91  17  84.14 

91  91  80.70 

91  8S  47.36 

81  39  48.81 

31  88  40.86 

31  S7  86.91 

31  41  8S.46 


0.164  91  46  80.08 
0.198  81  40  36.87 
0.383  31   68  38.18 


The  third  coiumn  shows  the  R.  A.  of  the  sun's  centre  at  Oreen- 
wich  mean  noon  of  eacli  day.  The  fourth  column  shows  the  hourly 
change  of  this  quantity  (9.815  on  Feb.  12).  At  Greenwich  0  hours 
the  sun's  R.  A.  was  21  ■>  44'"  10*.80.  Washington  is  fi^  ^  (6^.18) 
west  of  Greenwich.  At  Washington  mean  noon,  on  the  ISth,  the 
Greenwich  mean  time  was  S'*.  18.  0.815  X  5.18  is  SO'.SS.  This  isto 
be  added,  since  the  R  A.  is  increasing.  The  sun's  R.  A.  at  Wash- 
ington mean  noon  is  tlierefore  21^  45"  1*.15.  A  similar  process  will 
give  the  sun's  declination  for  Washington  mean  noop.  In  the  same 
manner,  the  R.  A.  and  Dec.  of  the  sun  for  any  place  whose  longitude 
is  iinown  can  be  found. 

The  column  "Equation  of  Time"  gives  the  quantity  to  be  sub- 
tracted from  the  Greenwich  mean  solar  time  to  obtain  the  Green- 
wich apparent  solar  time  (see  page  188).  Thus,  for  Feb.  1,  the 
Greenwich  mean  time  of  Greenwich  mean  nooc  is  0^  0*  0*.  Tlie 
true  sun  crossed  the  Greenwich  meridian  (apparent  noon)  at  28^  4ih 
08*.66on  the  preceding  day;  i.e.,  Jan.  81. 

When  it  was  O*  0"  ()•  of  Greenwicli  mean  time  on  Feb.  18,  it  was 
also  21''  SS"  40'.35  of  Greenwich  local  sidereal  time  (see  the  last 
column  of  the  table), 


L&i 


nneri*,  wu  present 


[  Noon. 


n 

» 

Sid«iwil 

time 
orrlRht 
Moenuon 

of 
meMiaun. 

0.818 

o.mt 

0.8B0 

B. 

80 
80 
80 

M.      S. 

48  91.70 
fiO  18.98 
54  14.81 

0.918 
0.188 
O.ISO 

90 
91 
81 

B8  11.97 
9    7.98 
8    4.48 

0.117 
0.064 
O.OM 

91 
91 

91 

10    1.08 
18  S7.M 
17  M.14 

0.080 
0.011 
O.Ott 

91 
91 
91 

81  BO.TO 
88  47.95 
80  48.81 

0.078 
0.104 
0.184 

91 
91 
91 

88  40.86 
87  88.91 
41  88.48 

0.184 
0.198 
0.888 

91 

81 

46  80.08 
40  86.57 
08  88.18 

centre  at  Oreen- 
shows  the  hourly 
eenwich  0  hours 
I  is  fi^  ^  (6^.18) 
on  the  12tb,  the 
S0-.86.  Thtoisto 
B  R.  A.  «t  Wash- 
lilar  process  will 
OP.  In  the  some 
i  whose  longitude 

kntltv  to  be  sub- 
»btafn  the  Qreen- 

for  Feb.  1,  the 
isOkO-O*.    Tlie 

noon)  at  38^  46" 

n  Feb.  18,  it  was 
time  (see  the  last 


CHAPTER  IV. 

MOTION  OF  THE  EARTH. 

AVOBHT  IDIAS  or  THE  PUUntTS. 

It  was  observed  by  the  ancients  that  whilr;  the  great 
mass  of  the  stars  maintained  their  positionn  volatiTdly  to 
each  other  month  after  month  and  year  aiter  year,  there 

re  visible  to  them  seven  heavenly  bodies  which  changed 
thc'ir  positions  relatively  to  the  stars  and  to  each  other. 
These  they  called  planets  or  wandering  stars.  It  was  found 
that  the  seven  planets  performed  a  very  slow  revolution 
around  the  celestial  sphere  from  west  to  east,  in  periods 
ranging  from  one  month  in  the  case  of  the  moon  to  thirty 
years  in  that  of  Saturn, 

The  idea  of  the  fixed  stars  being  set  in  a  solid  sphere  was 
in  perfect  accord  with  thei(  diamal  revolution  as  observed 
by  the  naked  eye.  But  it  was  not  so  with  the  planets. 
The  latter,  after  continued  observation,  were  found  to 
move  sometimes  backward  and  sometimes  forward;  and  it 
was  quite  evident  that  at  certain  periods  they  were  nearer 
the  earth  than  at  other  periods.  These  motions  were  en- 
tirely inconsistent  with  the  theory  that  they  were  fixed  in 
solid  spheres. 

These  planets  (which  are  visible  to  the  naked  eye), 
together  with  the  earth,  and  a  number  of  other  bodies 
which  the  telescope  has  made  known  to  us,  form  a  family 
or  system  by  themselves,  the  diro«nsioQ^  pf  which,  although 


ASrUOAOMK 


»i 


!i 


I  hi  i : 


inconceivably  greater  tliun  niiy  wliich  wo  Imve  to  doal  with 
at  the  surface  of  tlie  oiirtli,  uru  riuito  iiiBignitlcuiit  when 
compurod  with  tlio  distiincu  wliich  .separates  us  from  the 
fixed  stars.  Tiio  sun  being  the  gn-at  central  body  uf  this 
Bystom,  it  is  called  the  i<ol(tr  Si/«/nu.  There  are  eight 
large  planets,  of  which  the  earth  is  tlie  third  in  the  order  of 
distance  from  tbo  sun,  and  the  bodies  nil  perform  a  regular 
revolution  around  tlie  sun.  Jl  '  .  v,  the  n*  iirest,  jierfornis 
its  revolution  in  three  months;  An^dnne,  ilie  farthest,  in 
164  years. 

AHiriTAL  SXYOLVTIOir  OF  THE  EABTH. 

To  an  observer  on  >-1ie  earth  the  sun  seems  to  perform 
an  annual  revolution  :vmong  the  stars,  a  fact  which  has 
been  known  from  early  ages.  This  motion  is  due  to  the 
annual  revolution  of  the  earlli  round  the  sun. 

In  Fig,  29  let  S  represent  ihc  sun,  ABCD  the  orbit 
of  the  earth  around  it,  and  ('11  ^GH  the  sphere  of  the 
fixed  stars.  This  sphere,  being  supposed  infinitely  distant, 
must  be  considered  as  infinitely«larger  than  the  circle 
ABCD.  Suppose  now  that  1,  2,  3,  4,  5,  6  are  a  number 
of  consecutive  positions  of  the  earth  in  its  orbit.  The  line 
IS  drawn  from  the  sun  to  the  earth  in  the  first  position  is 
called  the  radius-vector  of  the  earth.  Suppose  this  line 
extended  infinitely  so  as  to  meet  the  celestial  sphere  in  the 
point  1'.  It  is  evident  that  to  an  observer  on  the  earth  at 
1  the  sun  will  appear  projected  on  the  sphere  in  the  dii'ec- 
tion  of  1';  when  the  earth  reaches  2  it  will  appear  in  the 
direction  of  2',  and  so  on.  In  other  words,  as  the  earth 
revolves  around  the  sun,  the  latter  will  seem  to  perform  a 
revolution  among  the  fixed  stars,  which  are  immensely 
more  distant  than  itself.     The  points  1',  2',  etc.,  can  be 


I  to  (IohI  with 
litlcunt  when 
U8  from  tho 
I  body  of  this 
.>ro  are  vight 
I  tho  urdorof 
orm  tiroguhtr 
•est,  iKjrforniH 
9  farthest,  in 


m. 

8  to  perform 
:;t  which  has 
is  due  to  the 

7D  the  orbit 
iphere  of  the 
litely  distant, 
in  the  circle 
ire  a  number 
lit.  The  hne 
rst  position  is 
lose  this  line 
sphere  in  the 
.  the  earth  at 

in  the  direc- 
ippcar  in  the 

as  the  earth 
to  perform  a 
e  immensely 
,  etc.,  can  be 


r 


^, 


*>.^< 


m 


b: 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0    ^1^  tti 

■tt  1^   12.2 

2*  u^  ip*" 


1.1 


S  1^   12.0 


11-25  iU  1 1.6 

IIII^B  nHI^^  wmM 


•J' 


HiotogFaphic 

ScMioes 

C(xpQFati0n 


23  WMT  MAM  STMMT 

W||if|||,N.Y.  14SM 


CIHM/ICMH 

Microfiche 

Series. 


CIHIVI/iCIVIH 
Collection  de 
microfiches. 


Canadian  Inttituta  for  Historical  MIcroraproductiona  /  Inatitut  Canadian  da  micrcraproductlona  hiatoriquas 


0m^ 


MOTIONS  OF  rUE  EARTH. 


83 


fixed  by  tbeir  relations  to  the  yarioug  fixed  stars,  whose 
places  are  known. 

It  is  also  evident  that  the  point  in  which  the  earth  would 
be  projected  if  viewed  from  the  sun  is  always  exactly 
opposite  that  in  which  the  sun  appears  as  projected  from 
the  earth.     Moreover,  if  the  earth  moves  more  rapidly  in 


Fia. ».— BsToLonoM  ow  rvm  Eaktb. 


some  points  of  its  orbit  than  in  others,  it  is  evident  that 
the  son  will  also  appear  to  move  more  rapidly  among  the 
stars,  and  tLut  the  two  motions  must  always  accurately 
porresppnd  to  each  other, 

The  rftdius-yeotor  of  the  earth  in  its  annual  course  de- 
iOrib«B  »  plane;,  wUich  in  the  figure  may  be  represents  by 


H 


ASTRONOMY. 


i. 

k 


that  of  the  paper.  This  plane  continued  to  infinity  in 
every  direction  will  cut  the  celestial  sphere  in  a  great  cir- 
cle ;  and  it  is  clear  that  the  sun  will  always  appear  to 
move  in  this  circle.  The  plane  and  the  circle  are  indiffer- 
ently termed  the  ecliptic.  The  plane  of  the  ecliptic  is  gen- 
erally taken  as  the  fundamental  one,  to  which  the  jjositions 
of  all  the  bodies  in  the  solar  system  are  referred.  It 
divides  the  celestial  sphere  into  two  equal  parts.  In  think- 
ing of  the  celestial  motions,  it  if-  convenient  to  conceive  of 
this  plane  as  horizontal.  Then  if  we  draw  a  vertical  line 
through  the  sun  at  right  angles  to  this  plane  (perpendicular 
to  the  plane  of  the.  paper  on  which  the  figure  is  represent- 
ed), the  point  at  which  this  line  intersects  the  celestial 
sphere  will  be  the  pole  of  the  ecliptic 

Let  us  now  study  the  apparent  annual  revolution  of  the 
sun  produced  by  he  real  revolution  of  the  earth  in  its  orbit. 

When  the  earth  is  at  1  in  the  figure  the  sun  will  appear 
to  be  at  1',  near  some  star,  as  drawn.  Now  by  the  diurnal 
motion  of  the  earth  the  sun  is  made  to  rise,  to  culminate, 
and  to  set  successively  for  each  meridian  on  the  globe.  This 
star  being  near  the  sun  rises,  culminates,  and  Bets  with  it; 
it  is  on  the  meridian  of  any  place  at  the  local  noon  of  that 
place  (and  is  therefore  not  visible  except  in  a  telescope).  The 
star  on  the  right-hand  side  of  the  figure  near  the  line  C8l 
prolonged  is  nearly  opposite  to  the  sun.  When  the  san  is 
rising  at  any  place,  that  star  will  be  setting;  when  the  sun 
is  on  the  meridian  of  the  place,  this  star  is  on  the  lower 
meridian;  when  the  sun  is  setting,  this  star  is  rising.  It 
is  about  180°  from  the  sun.  Now  suppose  the  earth  to 
move  to  2.  The  sun  will  be  seen  at  2',  near  the  star  there 
marked.  2'  is  east  of  1';  the  sun  appears  to  move  among 
fhe  stars  (in  consec[uenc«  of  the  CHrtb'B  annual  motion) 


to  infinity  in 
in  a  great  cir- 
lys  appear  to 
}  are  indiffer- 
cliptic  is  gen- 
i  the  ]>oBitions 

referred.  It 
ks.  In  think- 
to  conceive  of 
a  vertical  line 
perpendicular 
)  is  represent- 

the  celestial 

olution  of  the 

th  in  its  orbit. 

in  will  appear 

\)j  the  diurnal 

to  culminate, 

e  globe.    This 

I  sets  with  it; 

1  noon  of  that 

tlescope).  The 

the  line  CSl 

tien  the  san  is 

when  the  sun 

on  the  lower 

is  rising.     It 

the  earth  to 

the  star  there 

o  move  among 

^nual  motion) 


MOTIONS  OF  THE  EARTH. 


88 


from  west  to  east.  The  star  near  2'  will  rise,  culminate, 
and  set  with  the  sun  at  every  place  on  the  earth.  The  star 
near  1'  being  west  of  2'  will  rise  before  tlie  sun,  culminate 
before  him,  and  set  before  he  does. 

If,  for  example,  the  star  1'  is  near  the  equator  when  the 
lun  is  15°  east  of  it,  the  star  will  rise  about  1  hour  earlier 
than  the  sun.  When  the  sun  h  30°  east  of  it  (at  3',  for 
example),  the  star  will  rise  2  hours  before  the  sun.  When 
the  sun  is  90°  east  of  1',  the  star  will  rise  6  hours  before  the 
sun,  and  so  on.  That  is,  when  the  siin  is  rising  at  any 
place,  this  star  will  be  on  the  meridian  of  the  place.  When 
the  sun  appears  in  the  line  VCS  1  prolonged  to  the  right 
in  the  figure,  the  star  1'  will  be  on  the  meridian  at  mid- 
night,  and  is  then  said  to  be  in  opposition  to  the  sun.  It 
is  180°  from  it.  When  the  sun  appears  to  be  near  H,  the 
star  1'  will  be  about  45°  or  3  hours  east  of  the  sun.  Tlio 
sun  will  rise  first  to  any  place  on  the  earth,  and  the  star 
will  rise  3  hours  later,  say  at  9  a.m.  Finally  the  sun  will 
come  back  to  the  same  star  again  and  they  will  rise,  cnlmi- 
nate,  and  set  together. 

We  know  that  this  cycle  is  about  365  days  in  length. 
In  this  time  the  son  moves  360°,  or  about  1°  daily.  This 
cycle  is  perpetually  repeated.  Its  length  is  a  sidereal  year; 
that  is,  the  interval  of  time  required  for  the  sun  to  move 
in  the  sky  from  one  star  back  to  the  same  star  again  or  for 
the  earth  to  make  one  revolution  in  its  orbit  among  the 
stars. 

The  ancients  were  familiar  with  this  phenomenon.  They 
knew  most  of  the  brighter  stars  by  name.  The  heliacal 
rising  of  a  bright  star  (its  rising  with  Helios,  the  sun) 
uwlred  the  beginning  of  a  cycle.  At  the  end  of  it,  seasons 
«l4  oropn  aii4  the  periodical  floods  of  the  Nile  Iiad  repeal 


86 


ASTRONOMY. 


ed  themselves.  It  was  in  this  way  that '  le  first  accurate 
notions  of  the  year  arose. 

The  apparent  position  of  a  body  as  seen  from  the  earth 
is  called  its  geocentric  place.  The  apparent  position  of  a 
body  as  seen  from  the  sun  is  called  its  heliocentric  place. 

In  the  last  figure,  suppose  the  sun  to  be  at  S,  and  the 
earth  at  4.  4'  is  the  geocentric  place  of  the  sun,  and  0  is 
the  heliocentric  place  of  the  earth. 

The  Smr'B  Appabent  Path. 

It  is  evident  that  if  the  apparent  path  of  the  sun  lay  in 
the  equator,  it  would,  during  the  entire  year,  rise  exactly 
in  the  east  and  set  in  the  west,  and  would  always  cross  the 
meridian  at  the  same  altitude.  The  days  would  always  be 
twelve  hours  long,  for  the  same  reason  that  a  star  in  the 
equator  is  always  twelve  hours  above  the  horizon  and  twelve 
hours  below  it.  But  we  know  that  this  is  not  the  case,  the 
sun  being  sometimes  north  of  the  equator  and  sometimes 
south  of  it,  and  therefore  having  a  motion  in  declination. 
To  understand  this  motion,  suppose  that  on  March  19th, 
1879,  the  sun  had  been  observed  with  a  meridian  circle  and  a 
sidereal  clock  at  the  moment  of  transit  over  the  meridian  of 
Washington.  Its  position  would  have  been  found  to  be  this; 
Right  Ascension,  23"  SS"  83» ;  Declination,  0°  30'  south. 
Had  the  observation  been  repeated  on  the  20th  and  fol- 
lowing days,  the  results  would  have  been: 

March  20,  R  Ascen.  23"  59°'    2' ;  Dec.  0' 

21,  "  0"    2'°40»;      "    0° 

22,  "  0"    6"  19';     "    O' 

If  we  lay  these  positions  down  on  a  chart,  we  shall  fnd 
th^m  to  he  as  in  Fig.  30,  the  centra  of  the  sun  being  south 


'  6' South, 
17'  North, 
41'  North. 


%.. 


first  accurate 

)m  the  earth 
position  of  a 
Uric  place. 
\t  S,  and  the 
snu,  and  G  is 


ho  sun  lay  in 
',  rise  exactly 
rays  cross  the 
uld  always  be 
;  a  star  in  the 
on  and  twelve 
t  the  case,  the 
nd  sometiraes 
a  declination. 
I  March  19tb, 
ivn  circle  and  a 
lie  meridian  of 
and  to  be  this; 

0°  30'  south, 
I  20th  and  fol^ 

"  6' South, 
'  17'  North, 
Ul' North. 

we  shall  fnd 
in  being  soatk 


ifOrfONS  OF  THE  EARTH. 


87 


of  the  equator  in  the  first  two  positions,  and  north  of  it  in 
the  last  two.  Joining  the  successive  positions  by  a  line,  we 
shall  have  a  representation  of  a  small  portion  of  the  appa- 
rent path  of  the  sun  on  the  celestial  sphere,  or  of  the  ecliptic. 
It  is  clear  f  roin  the  observations  and  the  figure  that  the 
sun  crossed  the  equator  between  six  and  seven  o'clock  on 
Uie  afternoon  of  March  20th,  and  therefore  that  the  eqtia* 
tor  and  ecliptic  intersect  at  the  point  where  the  sun  was  at 
that  hour.  This  point  is  called  the  vernal  equinox,  the 
first  word  indicating  the  season,  while  the  second  expresses 


Fio.  SOi— Thb  Suit  OwMmia  tob  Equatob. 

the  equality  of  the  nights  and  days  wliich  occurs  when  the 
sun  is  on  the  equator.  It  will  be  remembered  that  this 
equinox  is  th6  point  from  which  right  ascensions  are  count- 
ed  in  the  heavens,  in  the  same  way  that  we  count  longi- 
tudes on  the  earth  from  Greenwich  or  Washington.  A 
sidereal  clock  at  any  place  is  therefore  so  set  that  the  hands 
shall  read  0  hours  0  minutes  0  seconds  at  the  moment 
when  the  vernal  equinox  crosses  the  meridian  of  the  place. 
Continuing  our  observations  of  the.  sun's -apparent  coarse 
for  six  months  from  March  20th  ^I)  Sept^ftiW  !23d,  vTe 


88 


ASmolfOMT. 


should  find  it  to  be  as  in  Fig.  31.    It  will  be  seen  that  Fig. 

30  corresponds  to  the  right> 
hand  end  of  31,  bnt  is  on  a 
much  larger  scale.  The  son, 
moving  along  the  great  circle 
of  the  ecliptic,  will  reach  its 
greatest  northern  declination 
about  June  21st.  This  point 
is  indicated  on  the  figure  as 
90°  from  the  vernal  equinox, 
nnd  is  called  the  summer  sol- 
stice. The  sun's  right  ascen- 
sion is  then  six  hours,  and  its 
declination  23^°  north.  The 
student  should  complete  the 
figure  by  drawing  the  half  not 
given  here. 

The  course  of  the  sun  now 
inclines  toward  the  south,  and 
it  again  crosses  the  equator 
about  September  22d  at  a  point 
diametrically  opposite  the  ver- 
nal equinox.  All  great  oirclee 
intersect  each  other  in  two  op- 
posite points,  and  the  ecliptic 
and  equator  intersect  at  the  two 
opposite  equinoxes.  The  equi- 
nox which  the  sun  crosses  <m 
September  22d  is  called  the 
autumnal  equitutx. 

During  the  six  months  from 
September  to  Much  the  nin'f 


een  that  Fig. 

0  the  right> 
bnt  is  on  a 

The  Ban, 

>  great  circle 

rill  reach  its 

declination 

This  point 

:lie  figure  as 

nal  equinox, 

summer  sol- 

right  ascen- 

ours,  and  its 

north.     The 

omplete  the 

the  half  not 

the  snn  now 
e  sonth,  and 
the  equator 
I2d  at  a  point 
>site  the  ver- 
great  circles 
er  in  two  op- 
tbe  eoliptio 
Bctatthetwo 
I.  The  equi- 
n  crosses  oa 

1  called  the 

months  from 
<sh  the  nm'f 


MTloifs  6F  fnn  MAiiTtt. 


fid 


bourse  is  a  counterpart  of  that  from  March  to  Septem- 
ber, except  that  it  lies  south  of  the  equator.  It  attains 
its  greatest  south  declination  about  December  22d,  in 
right  ascension  18  hours  and  south  declination  23°  30'. 
This  point  is  called  the  winter  solstice.  It  then  begins  to 
incline  its  course  toward  the  north,  reaching  the  vernal 
equinox  again  on  March  20th,  1880. 

The'  two  equinoxes  and  the  two  solstices  may  be  re- 
garded as  the  four  cardinal  points  of  the  sun's  apparent 
annual  circuit  around  the  heavens.  Its  passage  through 
these  points  is  determined  by  measuring  its  altitude  or  de- 
clination from  day  to  day  with  a  meridian  circle.  Since  in 
our  latitude  greater  altitudes  correspond  to  greater  declina- 
tions, it  follows  that  the  summer  solstice  occurs  on  the  day 
when  the  altitude  of  the  sun  is  greatest,  and  the  winter 
solstice  on  that  ^hen  it  is  leafit.  The  mean  of  these  alti- 
tudes is  that  of  the  equator,  and  may  therefore  be  found 
by  subtracting  the  latitude  of  the  place  from  90°.  The 
time  when  the  sun  reaches  this  altitude  going  north,  marks 
the  vernal  equinox,  and  that  when  it  reaches  it  going  south 
marks  the  autumnal  equinox. 

These  passages  of  the  sun  through  the  cardinal  points  have  been 
the  subjects  of  astronomical  observation  from  tlie  earliest  ages  on 
account  of  their  relations  to  the  change  of  the  seasons.  An  ingeni- 
ous metliod  of  finding  the  time  when  the  sun  reached  the  equinoxes 
was  used  by  the  astronomers  of  Alexandria  about  the  beginning  of 
our  era.  In  tlie  great  Alexandrian  Museum,  a  large  ting  or  wheel 
was  set  up  parallel  to  the  plane  of  the  equator;  in  other  words,  it 
was  so  fixed  that  a  star  at  the  pole  would  shine  perpendicularly  on 
the  wheel.  Evidently  its  plane  if  extended  must  have  passed  through 
the  east  and  west  points  of  the  horizon,  while  its  inclination  to  the 
vertical  was  equal  to  the  latitude  of  the  place,  which  was  not  far 
from  80°.  When  the  sun  reached  the  equator  going  north  or  south, 
and  shone  upon  this  wheel,  its  lower  edge  would  be  exactly  covered 
by  .the  shadow  of  the  upper  edge;  whereas  in  any  other  position  the 

i.. 


M 


AUfSoMMr. 


sun  would  shine  upon  the  lower  inner  edge.  Thus  the  time  at  which 
tlie  sun  reached  the  ecjuiuox  could  be  determined,  at  least  to  a  frac> 
ilon  of  a  day.  By  the  more  exact  methods  of  modurti  limes  it  can 
be  determined  within  less  than  a  minute. 

It  will  bo  seen  that  this  method  of  determining  the  annual  appar- 
ent course  of  tlic  sun  by  its  declination  or  altitude  is  entirely  inde- 
pendent of  its  relation  to  the  flxed  stars;  and  it  could  be  etiually  well 
bpplicd  if  no  stars  were  ever  visible.  There  arc,  tiiereforc,  two  en- 
tirely distinct  ways  of  finding  when  the  sun  or  tlic  earth  has  completed 
ita apparent  circuit  around  the  celestial  sphere;  tlie  one  by  the  transit 
instrument  and  sidereal  clock,  which  show  when  the  sun  returns  to 
the  tame  ponition  atnong  Vu  »tart,  the  other  by  the  measurement  of 
altitude,  which  shows  when  it  returns  to  the  tame  equinox.  By  the 
former  method,  already  described,  wc  conclude  that  it  has  completed 
an  annual  circuit  when  it  returns  to  the  same  star;  by  the  latter  when 
It  returns  to  the  same  equinox.  These  two  nietiiods  will  give  slightly 
different  results  for  the  length  of  the  year,  for  a  reason  to  be  here- 
after described. 

Tha  Zodiao  and  iU  DUisiou. — The  zodiac  is  a  belt  in  the  heavens, 
commonly  considered  as  extending  some  8'  on  eucli  side  of  the 
ecliptic,  and  therefore  about  16°  wide.  The  planets  known  to  the 
ancients  are  always  seen  within  this  belt.  At  a  very  early  day  the 
zodiac  was  mapped  out  into  twelve  signs  known  as  the  signt  of  the 
todiae,  the  names  of  which  have  been  handed  down  to  the  present 
time.  Each  of  these  signs  was  supposed  to  be  the  seat  of  a  constella- 
tion after  which  it  was  called.  Commencing  at  the  vernal  eq;;!sox, 
the  first  thirty  degrees  through  which  the  sun  passed,  or  the  region 
among  the  stars  in  wliich  it  was  found  during  tlie  month  following, 
was  called  the  sign  Aries.  The  next  thirty  degrees  was  called 
Taurus.  The  names  of  all  the  twelve  signs  in  their  proper  order, 
with  the  approximate  time  of  the  sun's  entering  upon  each,  are  as 
follows: 


Ariet,  the  Ram, 
Taurus,  the  Bull, 
Gemini,  the  Twins, 
Caneer,  the  Crab, 
Leo,  the  Lion, 
Virgo,  the  Virgin, 
L^ra,  the  Balance, 
Seorpius,  the  Scorpion, 
Sagittarius,  the  Archer, 
Gaprieomus,  the  Goat, 
Aquarius,  the  Watcr-be.-.rer, 
Pisces,  the  Fishes, 


March  20. 
April  20. 
May  20. 
June  21. 
July  22. 
August  22. 
September  22. 
October  28. 
November  28. 
December  21. 
January  20. 
Februaiy  19. 


e  time  at  which 

least  to  a  frac> 

rti  limes  it  can 

3  annual  appar- 
is  entirely  inde- 
be  etiuully  well 
erefore,  two  en- 
I  lias  completed 
le  by  the  transit 
sun  returns  to 
aeaaurement  of 
juinojc.  By  the 
t  has  completed 
the  latter  when 
rill  give  slightly 
son  to  be  here- 
in the  heavens, 
ich  side  of  the 
I  known  to  the 
y  early  day  the 
the  signt  of  the 
1  to  the  present 
t  of  a  constclla- 
rernal  equinox, 
i,  or  the  region 
)nth  following, 
ees  was  called 
r  proper  order, 
on  each,  ore  as 


r23 

B. 

r28. 

•21. 

!0. 

19. 


koftoifS  OF  fits  XARta. 


dl 


Each  olP  these  signs  coincides  roughly  with  a  constellation  in  the 
heavens;  and  thus  there  arc  twelve  constellations  called  by  the 
names  of  these  signs,  but  the  signs  and  the  constellations  no  longer 
correspond.  Altiiough  tlie  sun  now  crosses  the  equator  and  enters 
the  $ign  Aries  on  the  20th  of  March,  he  does  not  reach  the  eonttella. 
lion  Aries  until  nearly  a  month  later.  This  arises  from  the  precea- 
sion  of  the  equinoxes,  to  be  explained  hereafter. 

OBUQinTT  07  THS  SOIimO. 

We  have  already  stated  that  when  the  sun  is  at  the  snm- 
faior  solstice  it  is  about  23^°  north  of  the  equator,  and  when 
at  the  winter  solstice,  about  2'6^"  south.  This  shows  that 
the  ecliptic  and  equator  make  an  anple  of  about  23^°  with 
each  other.  This  angle  is  called  the  obliquity  of  the  eclip- 
tic, and  its  determination  is  very  simple.  It  is  only  neces- 
sary to  find  by  repeated  observation  the  sun's  greatest  north 
declination  at  the  summer  solstice,  and  its  greatest  south 
declination  at  the  winter  solstice.  Either  of  these  declina- 
tions, which  must  be  equal  if  the  observations  are  accurate- 
ly made,  will  give  the  obliquity  of  the  ecliptic.  It  has  been 
continually  diminishing  from  the  earliest  ages  at  a  rate  of 
about  half  a  second  a  year,  or,  more  exactly,  about  47'  in 
a  century.  This  diminution  is  due  to  the  gravitating 
forces  of  the  pl^iets,  and  will  continue  for  several  thousand 
years  to  come.  It  will  not,  however,  go  on  indefinitely, 
but  the  obliquity  will  only  oscillate  between  comparatively 
narrow  limits. 

In  the  preceding  paragraphs  we  have  explained  the 
apparent  annual  circuit  of  the  sun  relative  to  the  equator, 
and  shown  how  the  seasons  depend  upon  this  circuit.  In 
order  that  the  student  may  clearly  grasp  the  entire  subject, 
it  is  necessary  to  show  the  relation  ol  these  apparent  move- 
ments to  the  actual  movement  of  the  earth  around  the 
van. 


1 


To  understand  the  relation  of  the  equator  to  the  ecliptic,  we  must 
remcmlier  that  tiio  cele«tinl  pole  and  tlie  celostiitl  equator  hare  really 
no  ruferenco  whatever  to  the  heavens,  but  depend  solely  on  the  direc- 
tion of  tlie  earth's  axis  of  rotation.  Tlie  polo  of  the  lieitvens  is  noth- 
ing more  than  that  |K>int  of  tlio  cele'tdal  sphere  toward  which  tlie 
earth's  axis  happens  to  point.  If  the  direction  of  this  axis  changes,  the 
position  of  tlie  eeleHtial  pole  among  the  stars  will  change  also ;  tliough 
to  an  observer  on  the  earth,  unconscious  of  tlie  change,  it  would 
■eem  as  if  tlie  starry  sphere  moved  while  the  pole  remained  at  rest. 
Again,  tlie  celestial  equator  being  merely  the  great  circle  in  which 
the  plane  of  the  earth's  equator,  extended  out  to  infinity  In  every 
direction,  cuta  the  celestial  sphere,  any  change  in  tlie  direction  of  ilie 
pole  of  the  earth  would  necessarily  change  the  position  of  ilie  equator 
among  the  stars.  Now  the  positions  of  the  celestial  pole  and  the 
celestial  equator  among  the  stars  seem  to  remain  unchanged  tiirough- 
out  the  year.  (There  is,  indeed,  a  minutd  change,  but  it  does  not 
affect  our  present  reasoning.)  This  sliows  that,  as  the  earth  revolves 
around  the  sun,  its  axis  is  constantly  directed  toward  nearly  the 
•amo  point  of  the  celestial  sphere. 


Thx  Siaiovk 

The  conclnsions  to  which  we  are  thus  led  respecting  the 
real  revolution  of  the  earth  are  shown  in  Fig.  32.  Here  8 
represents  the  sun,  with  the  orbit  of  the  earth  surrounding  it, 
but  viewed  nearly  edgeways  so  as  to  be  much  foreshortened. 
A  B  CD  are  tlic  four  cardinal  positions  of  the  earth  which 
correspond  to  the  cardinal  points  of  the  apparent  path  of  the 
Bun  already  described.  In  each  figure  of  the  earth  iV^  is 
the  axis,  N  being  its  north  and  8  its  south  pole.  Since 
this  axis  points  in  the  same  direction  relative  to  the  stars 
during  an  entire  year,  it  follows  that  the  different  lines 
NS  are  all  parallel.  Again,  since  the  equator  does  not 
coincide  with  the  ecliptic,  these  lines  are  not  perpendicular 
to  the  ecliptic,  but  are  inclined  from  this  perpendicular  bj 
23i°. 

When  the  earth  is  at  A  the  sun's  north-polar  distance  (the 


i 


cliptlc,  we  mutt 
lutor  bnre  renlly 
lily  OD  the  direc- 
lieaveDH  Is  iiotk- 
wrard  wliicli  the 
kxis  changes,  the 
ge  nl84> ;  though 
muge,  il  wouhl 
iniiliied  at  rcHt. 
circle  In  which 
nflnity  In  every 
direction  of  the 
n  of  the  equator 
al  pole  and  the 
innged  through- 
but  It  does  not 
e  eiirth  ruvotves 
rurd  nearly  the 


'especting  the 

32.    Here  S 

irroiinding  it, 

oreshortened. 

3  earth  which 

tit  path  of  the 

earth  NSin 

pole.    Since 

)  to  the  stars 

ifferent  linei 

iter  does  not 

lerpendicalar 

[leudicuhu*  bj 

distance  (the 


MOTIOm  oy  THB  BAni'lt.  08 

angle  at  the  centre  of  the  earth  at  .1  between  the  lines  to 
the  north  polo  and  to  the  sun)  is  li:^";  ut  //  it  is  00°;  at 
C  it  is  66^°;  at  D  it  is  uguin  00°,  and  between  60^  and 
113^°  the  north-polar  distance  continunlly  yaries.  This 
may  bo  plainer  if  the  student  draws  the  lines  SA,  S H, 
SC,  SD,  and  prolongs  the  lines  N8  at  each  position  of 
the  earth. 

Now  the  snn  shines  on  only  one  half  of  the  earth;  viz., 
that  hemisphere  turned  toward  him.  This  hemisphere  is 
left  bright  in  each  of  the  figures  of  the  earth  at  A,  B,  V,  D. 


Fw.  St.— Oaohh  <mp  tbb  SiAaon. 


Oonsider  the  diagram  at  A,  and  remember  that  the  earth 
is  turning  round  so  that  every  observer  is  carried  round 
his  parallel  of  latitude  every  24  hours.  The  parallels  are 
drawn  in  the  eat,  and  it  is  plain  that  a  person  near  N  will 
remain  in  darkness  all  the  24  hours ;  any  one  in  the  north- 
em  hemisphere  is  leas  than  half  the  time  in  the  light — that 
is,  the  snn  is  less  than  half  the  time  above  his  horizon — 
and  a  person  in  the  southern  hemisphere  is  mart  than  half 
the  time  in  the  light.    At  the  equator  the  days  and  nighti 


■■! 


04 


ABTRomnr. 


are  always  equal.  At  the  scurh  pole  it  is  perpetual  day. 
The  spectator  near  the  south  pole  is  carried  jound  in  a 
parallel  of  latitude  which  is  perpetually  shined  upon. 
This  is  the  winter  solstice  (midwinter  in  the  northern 
hemisphere,  midsummer  in  the  southern). 

Next  suppose  the  cartli  at  ^ :  Bis  00°  ftom  A ;  that  is, 
3  months  later.  The  sun's  rays  just  graze  the  north  and 
south  poles;  each  parallel  of  latitude  is  half  light  and  half 
dark ;  the  days  and  nights  are  equal.  This  is  the  equinox 
of  spring — the  vernal  equinox.  The  sun's  north-polar  dis- 
tance is  90°.  At  C  we  have  the  summer  solstice  (summer 
in  the  northern  hemisphere,  Avinter  in  the  sonthcrn). 
Here  is  perpetual  day  at  the  north  pole,  perpetual  night  at 
the  south;  long  days  to  nil  the  northern  hemisphere,  long; 
nights  in  the  southern.  Three  months  later  wc  have  the 
autumnal  equinox  at  D.  ,     * ' . 

Thid  change  of  the  seasons  depends  upon  the  chaugeof 
the  sun's  north-polar  distance. 

The  exact  phenomena  at  each  place  maybe  studied  by 
constructing  a  diagram  for  the  latitude  of  that  place  (roe 
page  42)  and  assuming  the  sun's  north-polar  distance  as 
.fellows:.      ...  ...    -    ,„...,, 


March  31, 

N.P.D. 

90°, 

Vernal  Equinox. 

June  30, 

N.P.D. 

66i, 

Summer  Solstice. 

September  31, 

N.P.D. 

90, 

Autumnal  Equinox. 

December  21, 

N.P.D. 

113i, 

Winter  Solstice. 

Two  such  diagrams  are  given  in  the  text-book  (page  28). 
The  student  should  be  able  to  pro^'e  that  thd  sun  is  always 
in  the  zenith  of  some  place  in  the  torrid  zone. 


4^ 


s  perpetual  day. 
-riedjound  in  a 
y  shined  upon, 
n  the  northern 

From  A ;  that  is, 
a  the  north  and 
[flight  and  half 
8  is  the  equinox 
north-polar  dis- 
solstice  (summer 
the  Bonthcrn). 
irpetual  night  at 
leniisphere,  longj, 
iter  wo  have  the 

m  the  change  of 

ly  be  studied  by 
!  that  place  (eeo 
Dlar  distance  as 


1  Equinox, 
ler  Solstice, 
inal  Equinox. 
r  Solstice. 

-book  (page  28). 
the  sun  is  always 
>ne. 


MOTIONS  OF  THE  EARTH.  96 


Celestial  Latitude  ahb  Lohoitubs. 

To  describe  the  positions  of  the  sun  and  planets  in  space 
we  need  two  new  co-ordinates. 

The  Celestial  Latitude  of  a  star  is  its  angular  distance 
north  or  south  of  the  ecliptic. 

The  Celestial  Longitude  of  a  star  is  its  angular  distance 
from  the  vernal  equinox  measured  on  the  ecliptic  from 
west  to  east.  Having  the  right  ascension  and  declination 
of  a  body  (which  can  be  had  by  observation),  we  can  com- 
pute its  celestial  latitude  and  longitude.  These  co-ordinates 
are  no  longer  observed  (as  they  were  by  the  ancients),  but 
deduced  from  observations  of  right  ascension  and  declina- 
tion. 


t'4J 


.irt....i"- 


•■wp" 


CHAPTER  V. 


THE  PLANETARY  MOTIONS. 

AnAMxn  Airs  Rial  MoTion  ov  the  PiAnm 

DefliiitieiUL — The  soiar  syBtem  compriaes  a  number  of 
bodies  of  rarious  orders  of  magnitode  and  distance,  sub- 
jected to  many  complex  motions.  Oar  attention  will  be 
particularly  directed  to  the  motions  of  the  great  planets. 
These  bodies  may,  with  respect  to  their  apparent  motions, 
be  divided  into  three  classes. 

Speaking,  for  the  present,  of  the  sun  as  a  planet,  the 
first  class  comprises  the  8un  and  moon.  We  have  seen  that 
if,  upon  a  star  chart,  we  mark  down  the  positions  of  the 
sun  day  by  day,  they  will  all  fall  into  a  regular  circle  which 
marks  out  the  ecliptic.  The  monthly  course  of  the  moon 
is  found  to  be  of  the  same  nature;  and  although  its  motion 
is  by  no  means  uniform  in  a  month,  it  is  always  toward  the 
east,  and  always  along  ov  very  near  a  certain  great  circle. 

The  second  class  comprises  Venus  and  Mercury.  The 
apparent  motion  of  these  bodies  is  an  oscillating  one  on 
each  side  of  the  sun.  If  we  watch  for  the  appearance  of 
one  of  these  planets  after  sunset  from  evening  to  evening, 
we  shall  find  it  to  appear  above  the  western  horizon.  Night 
after  night  it  will  be  farther  and  farther  from  the  sun  until 
it  attains  a  certain  maximum  distance;  then  it  will  appear 
to  r^tuni  towards  the  sun  a^n,  and  for  a  whil^  tQ  ^  loit 


THE  PLANETARY  MOTIONS. 


97 


:  Plaibts. 

1  a  number  of 
distance,  snb- 

tention  will  be 
great  planets. 

arent  motions, 

I  a  planet,  the 
have  seen  that 
ositions  of  the 
ar  circle  which 
B  of  the  moon 
ugh  its  motion 
ays  toward  the 
I  great  circle. 
)£ereHry.  The 
Hating  one  on 
appearance  of 
ing  to  evening, 
srizon.  Night 
a  the  sun  until 
I  it  will  appear 
rhil?  tQ  b9  loit 


in  its  rays.  A  few  days  later  it  will  reappear  to  the  west 
of  the  sun,  and  thereafter  be  visible  in  the  eastern  horizon 
before  sunrise.  In  the  case  of  Mercury  the  time  required 
for  one  complete  oscillation  back  and  forth  is  about  four 
months;  and  in  the  case  of  Venus  it  is  more  than  a  year 
and  a  half. 

The  third  class  comprises  Mars,  Jupiter,  and  Saturn,  as 
well  as  a  great  number  of  planets  not  visible  to  the  naked 
eye.  The  general  or  average  motion  of  these  planets  is 
toward  the  oast,  a  complete  revolution  in  the  celestial 
sphere  being  performed  in  times  ranging  from  two  years  in 
the  case  of  Mars  to  164  years  in  that  of  Neptune.  But, 
instead  of  moving  uniformly  forward,  they  seem  to  luvre  a 
swinging  motion;  first,  they  move  forward  or  toward  the 
east  through  a  pretty  long  wrc,  then  backward  or  westward 
through  a  short  one,  then  forward  through  a  longer  one, 
etc.  It  is  by  the  excess  of  the  longer  arcs  over  the  shorter 
ones  that  the  circuit  of  the  heavens  is  made. 

The  general  motion  of  the  sun,  moon,  and  planets  among 
the  stars  being  toward  the  east,  motion  in  this  direction  is 
tilled  direct;  motions  toward  the  west  are  called  retrograde. 
j  nring  the  periods  between  direct  and  retrograde  motion 
the  planets  will  for  a  short  time  appear  stationary. 

The  planeta  Venus  and  Mercury  are  said  to  be  at  greatest 
elongation  when  at  their  greatest  angular  distance  from  the 
sun.  The  elongation  which  occurs  with  the  planet  east  of 
the  sun,  and  therefore  visible  in  the  western  horizon  after 
sunset,  is  called  the  eastern  elongation,  the  other  the  west- 
em  one. 

A  planet  is  said  to  be  in  .  onjunction  with  the  sun  when 
it  is  in  the  same  direction  as  seen  from  the  earth,  or  when, 
«■  it  awm  to  pass  b^  the  sun,  it  approaches  nearest  U>  it. 


1,  i 


m 


ASTRONOMY. 


It  is  said  to  be  in  opposition  to  the  sun  when  exactly  in  the 
opposite  direction — rising  when  the  Eun  sets,  and  vice 
versa.*  If,  when  a  planet  is  in  con  junction,  it  is  between 
the  earth  and  the  sun,  the  conjunction  is  said  to  be  an 
inferior  one;  if  beyond  the  sun,  it  is  said  to  be  superior. 


i 


Fm.  as.— Omn  of  tbs  Fijuim. 

Axntngements  and  Motions  of  the  Planeti.— The  sun  i» 
tlie  real  centre  of  the  solar  system,  and  the  planets  proper 
revolve  around  it  as  the  centre  of  motion.  The  order  of 
the  five  innermost  large  planets,  or  the  relative  position  of 

*  A  planet  is  in'  oonjunetion  with  tbe  sun  when  it  has  the  aame 
geocentric  longitude;  in  oppoeition  wUen  the  longitudes  differ  l^\ 


THE  PLANETAliY  MOTIONS. 


9% 


exactly  in  the 
ets,  and  vice 
it  is  between 
said  to  be  an 
je  superior. 


k — ^The  sun  Js 

ilanets  proper 

The  order  of 

ye  position  of 

it  has  the  aamie 
uclM  differ  l^\ 


their  orbits,  is  shown  in  Fig.  33.  These  orbits  are  all 
nearly,  but  not  exactly,  in  the  same  plane.  The  planets 
Mercury  and  Vemis  which,  as  seen  from  the  earth,  never 
appear  to  recede  very  far  from  the  sun,  are  in  reality  those 
which  revolve  inside  the  orbit  of  the  earth.  The  planets 
of  the  third  class,  wliich  perform  their  circuits  at  all  dis- 
tances from  the  sun,  are  what  we  call  the  superior  planets, 
and  are  more  distant  from  the  sun  than  the  earth  is.  Of 
these  the  orbits  of  Mars,  Jupiter,  and  a  swarm  of  telescopic 
planets  are  shown  in  the  figure;  next  outside  of  Jupiter 
comes  Saturn,  the  farthest  planet  readily  visible  to  the 
nakcid  eye,  and  then  Uranus  and  Neptune,  telescopic  plan- 
ets. On  the  scale  of  Fig.  38  the  orbit  of  Neptune  wonld 
be  more  than  two  feet  in  diameter.  Finally,  the  moon  is 
a  small  planet  revolving  around  the  earth  as  its  centre,  and 
carried  with  the  latter  as  it  moves  around  the  sun. 

Inferior  planets  are  those  whose  orbits  lie  inside  that  of 
the  earth,  as  Mercury  and  Venus. 

Superior  planets  are  those  whose  orbits  lie  outside  that 
of  the  earth,  as  Mars,  Jupiter,  Saturn,  etc 

The  farther  a  planet  is  situated  from  the  sun  the  slower 
is.  its  orbital  motion.  Therefore,  as  we  go  from  the  ntn, 
the  periods  of  i-evolution  are  longer,  for  the  double  reason 
that  the  planet  iias  a  larger  orbit  to  describe  abd  iAbves 
more  slowly  in  its  orbit.  It  is  to  this  slower  motion  of  the 
outer  planets  that  the  occasional  apparent  retrograde  mo* 
tion  of  the  planets  is  due,  as  may  be  seen  by  studying  Fig. 
31.  The  apparent  position  of  a  planet,  as  seen  from  the 
earth,  is  determined  by  the  lino  joining  the  earth  and 
planet.  Supposing  this  line  to  be  continued  so  as  to  inter- 
sect the  celestial  sphere,  the  apparent  motion  of  the  planet 
wiU  be  defiacd  by  the  motion  of  the  point  in  which  the  line 


I  ti 


■TSS 


100 


A8TR0N0MT. 


intersects  the  sphere.     If  tliis  motion  is  toward  the  east,  it 
is  direct ;  if  toward  the  west,  retrograde. 

The  Apparent  Kotion  of  a  Superior  Planet.— In  the  figure 
let  S  bo  the  sun,  ABODE F  tlie  orbit  of  the  earth,  and 
HIKLMN  the  orbit  of  a  superior  planet,  as  Mar%. 
When  the  earth  is  at  A  suppose  Mars  to  be  at  H,  and  let 
B  and  /,  C  and  iT,  B  and  Z,  E  and  il,  F  and  JV  be  corre- 
sponding positions.    As  the  earth  moves  faster  than  Mart 


rw.si 

the  arcs  AB,  EC,  etc.,  correspond  to  greater  angles  at  the 
centre  than  HI,  IK,  etc. 

When  the  earth  is  at  ^,  Mars  will  be  seen  on  the  celestial 
sphere  at  the  apparent  position  0.  When  the  earth  is  at 
B,  Mars  will  be  seen  at  P.  As  the  earth  describes  AB, 
Mars  will  appear  to  describe  OP  moving  in  the  same  direc- 
tion as  the  earth's  orbital  motion;  i.e.,  direct.  When  the 
earth  is  at  C,  Mars  is  at  K  (in  opposition  to  the  sun),  and 
ite  motion  is  retrograde  along  the  small  arc  beyond  QP  iu 


i  the  east,  it 

[n  the  figure 
0  earth,  and 
b,  as  Mara, 
;  H,  and  let 
JV  be  corre- 
r  than  Mart 


mgles  at  the 

the  celestial 
I  earth  is  at 
•scribes  AB, 
)  same  direo- 
When  the 
he  sun),  and 
>yond  QP  ii| 


THB  PLANETARY  MOTIONS. 


101 


the  figure.  When  the  earth  reaches  D  the  planet  has  fin- 
ished its  rctrogi-ade  arc.  As  the  earth  moves  from  D  io  E 
the  planet  moves  from  L  to  M,  and  the  lines  joining  earth 
and  planet  are  parallel  and  correspond  to  a  fixed  position 
on  the  celestial  sphere.  The  planet  is  at  a  station.  As  the 
earth  moves  from  Eio  Fihe  apparent  motion  of  Mara  is 
direct  from  Q  io  R;  and  in  the  same  way  the  apparent 
motion  of  any  outer  planet  can  be  determined  by  drawing 
its  orbit  outside  of  the  earth's  orbit  ABODE  Fond  laying 
off  on  this  orbit  positions  which  correspond  to  the  points 
ABCDEF  and  joining  the  corresponding  positions.  It 
will  be  found  that  all  outer  planets  have  a  retrograde  mo- 
tion at  opposition,  etc. 

The  Apparent  Motion  of  an  Inferior  Planet— To  deter- 
mine the  corresponding  phenomena  for  an  inferior  planet 
the  same  figure  may  be  used.    Suppose  HIKLMto  be 
the  orbit  of  the  earth,  mdAB  CD  EF  the  orbit  of  Mer- ; 
eury,  and  suppose  iSTand  A,  /and  B,  etc.,  to  bo  corre- ; 
spending  positions.    Suppose  HA  to  he  tangent  to  Mar- '' 
eury' a  orbit.    The  angle  AHS  is  the  elongation  of  Mer-'l 
eury,  and  it  is  the  greatest  elongation  it  can  ever  have,  i 

Let  the  student  construct  the  apparent  positions  of  Mar* ' 
eury  as  seen  from  the  earth  from  the  data  given  in  the : 
figure.    From  the  apparent  positions  he  can  determine  the 
apparent  motions.    As  Mercury  moves  from  ^^  its  ap- 
parent motion  is  direct    On  both  sides  of  the  inferior  con- '. 
junction  C  its  motion  is  retrograde.    From  D  to  E  it  is 
stationary.    Also  let  him  construct  the  apparent  positions 
of  the  ran  at  different  times  by  drawing  the  lines  H8,  IS, 
K8,  etc.,  towards  the  right    The  angles  between  the  ap- 
parent positions  of  Mercury  and  the  sun  will  be  the  elonga- 
tions of  Mercury  at  yarious  times. 


102 


A8TR0N0MT. 


TkMry  of  KplojrelM.— Complicated  as  tlie  apparent  motions  of  the 
planets  were,  it  wus  seen  by  tlic  ancient  astruuomers  tliat  tliey  could 
be  represented  by  n  combinatiun  of  two  motions.  First,  a  small  circle 
or  epicycle  was  supposed  to  move  around  the  earth  (not  the  sun) 
with  a  regular,  though  not  uniform,  forward  motion,  and  then  the 
planet  was  supposed  to  move  around  the  circumference  of  this  circle. 
The  relation  of  this  theory  to  the  true  one  was  this:  The  regular 
forward  motion  of  the  epicycle  represents  the  real  motion  of  the 
pinnet  around  the  sun,  while  the  motion  of  the  planet  around  the 
circumference  of  the  epicycle  is  an  apparent  one  arising  from  the 

revolution  of  the  eartli  around  the 
sun.  To  explain  this  we  must  under- 
stand some  of  the  laws  of  relative  mo- 
tion. 

It  is  fuiniliitrly  known  thut  if  an 
observer  in  unconscious  motion  looks 
upon  an  object  at  rest,  the  object  will 
appear  to  him  to  move  in  a  direction 
opposite  that  in  wiilcli  he  moves.    As 
a  result  of  this  law,  if  the  observer  is 
unconsciously  describing  a  circle,  an 
object  at  rest  will  appear  to  him  to 
describe  a  circle  of  equal  size.    This 
is  shown  by  the  following  figure.    Let 
6' represent  the  sun,  and  ABC  DBF 
the  orbit  of  the  earth.     Let  us  sup- 
pose the  observer  on  the  earth  carried 
around  in  this  orbit,  but  imagining 
himiielf  nt  rest  at  8,  the  centre  of  mo- 
tion.   Suppose  he  keeps  observing  the 
direction  and  distance  of  the  planet  P, 
which  for  the  present  we  suppose  to 
be  at  rest,  since  it  is  only  the  relative 
motion  that  we  shall  have  to  consider. 
When  the  observer  is  at  A  he  really 
aees  the  planet  in  a  direction  and  distance  A  P.  but  imagining  himself 
at  a  he  thinks  he  see  the  planet  at  the  point  a  determined  by  drawing 
a  Une  8a  parallel  and  equal  to  ^  P.    As  he  passes  from  ^  to  B  the 
planet  will  seem  to  him  to  move  in  the  opposite  direction  from  a  to 
b,  the  point  b  being  determined  by  drawing  Sb  equal  and  parallel 
to  BP     As  he  recedes  from  the  planet  through  the  arc  B  CD,  the 
planet  seems  to  recede  from  him  through  bed;  and  while  he  movee 
from  left  to  right  through  DB  the  phinet  seems  to  move  from  ri^t 


no 


PlAifETAttr  MOTIONS. 


108 


itioDB  of  the 

It  tliey  could 

a  smull  circle 

not  the  sun) 

ind  then  the 

of  this  circle. 

Tlic  regular 

lOtion  of  tlie 

;  around  the 

ng  from  the 

around  the 

must  under- 

f  relative  mo- 

1  thut  if  an 
motion  looks 
le  object  will 
n  a  direction 
I  moves.    As 
e  observer  is 
;  a  circle,  an 
ar  to  him  to 
il  size.    This 
g  figure.    Let 
ABCDEP 
Let  us  sup- 
enrth  carried 
ut  imagining 
centre  of  mo- 
observing  the 
the  planet  P, 
re  suppose  to 
y  the  relative 
e  to  consider. 
i  A  he  really 
pning  himself 
3d  by  drawing 
m  ^  to  B  the 
ion  from  a  to 
1  and  parallel 
arc  S  CD,  the 
rhile  he  movea 
ve  from  ri^t 


to  left  through  de.  Finally,  as  he  approachv'>8  the  planet  through 
the  arc  efa  the  planet  seems  to  approach  him  through  EFA,  and 
when  lie  returns  to  A  the  planet  will  appear  nt  A,  as  in  the  liegln- 
ning.  Thus  tlio  planet,  though  really  at  rest,  would  seem  to  him  to 
move  over  the  circle  abcdef  corresponding  to  that  in  which  the 
observer  himself  was  carried  around  the  sun. 

The  planet  being  really  in  motion,  it  is  evident  that  the  combined 
effect  of  the  real  motion  of  the  planet  and  the  apparent  motion 
around  the  circle  abedefviW  be  represented  by  carrying  the  centre 
of  this  circle  P  along  the  true  orbit  of  the  planet.  The  motion  of 
the  eartii  being  more  rapid  than  that  of  an  outer  planet,  it  follows 
that  the  apparent  motion  of  the  planet  through  a  6  is  more  rapid 
tlian  the  real  motion  of  P  along  the  orbit.  Hence  in  this  part  of  the 
orbit  tiie  movement  of  the  planet  will  be  retrograde.  In  every  other 
part  it  will  be  direct,  l»ecause  the  progressive  motion  of  P  will  at 
least  overcome,  sometimes  be  added  to,  tlie  apparent  motion  around 
the  circle. 

In  the  ancient  astronomy  the  apparent  small  circle  abedefyru 
called  the  epieyele. 

In  the  case  of  the  inner  planets  Mercury  and  Vmu$  the  relation  of 
the  epicycle  to  the  true  orbit  is  reversed.  Here  the  epicyclic  motion 
is  that  of  the  planet  round  its  real  orbit;  that  is,  the  true  orbit  of  the 
planet  around  the  sun  was  itself  taken  for  the  epicycle,  while  the 
forward  motion  was  really  due  to  the  apparent  revolution  of  the  sun 
produced  by  the  annual  motion  of  the  earth. 

By  constructing  a  figure  for  this  case  the  student  can  readily  see 
how  tills  comes  about. 

Although  the  obseryations  of  two  thousand  yean  ago 
could  be  tolerably  well  explained  by  these  epicycles,  yet 
with  eyery  increase  of  accuracy  in  observation  new  compli- 
cations had  to  be  introduced,  until  at  the  time  of  Copsb- 
Hicus  (164?)  the  confusion  was  very  great. 

The  Copemioan  System  of  the  World.— Cofebkicus  re- 
vived a  belief  taught  by  some  of  the  ancients  that  the  sun 
was  tite  centre  of  the  system,  and  that  the  earth  and  plan- 
ets moved  about  him  in  circular  orbits.  While  this  was  a 
atq>,  and  a  great  step,  forward,  purely  circular  orbits  for 
the  planets  would  not  explain  all  the  facta. 


r» 


104 


ASTRONOMY. 


From  the  time  of  Copernicus  (1543)  till  that  of  Kep- 
ler and  Galileo  (1600  to  1630)  the  whole  question  of  the 
true  system  of  the  universe  was  in  debate.  The  circular 
orbits  introduced  by  Copernicus  also  required  a  complex 
system  of  epicycles  to  account  for  some  of  the  observed 
motions  of  the  planets,  and  with  every  increase  in  accuracy 
of  observation  new  devices  had  to  be  introduced  into  thb 
system  to  account  for  the  new  phenomena  observed.  In 
short,  the  system  of  Copernicus  accounted  for  so  many 
facts  (ad  the  stations  and  retrogradatious  of  the  planets) 
that  it  could  not  bo  rejected,  and  had  so  many  difficulties 
that  without  modification  it  could  not  be  accepted. 

KmjtB's  Laws  or  PLAniiBT  Monov. 

Kepler  and  Galileo.— Kepler  (bom  1571,  d.  1630)  was 
a  genius  of  the  first  order.  He  had  a  thorough  acquaint- 
ance with  the  old  systems  of  astronomy  and  a  thorough  be- 
lief  in  the  essential  accuracy  of  the  Oopernican  system, 
whose  fundamental  theorem  was  that  the  sun  and  not  the 
earth  was  the  centre  of  our  system.  He  lived  at  the  same 
time  with  Galileo,  who  was  the  first  person  to  observe  the 
heavenly  bodies  with  a  telescope  of  his  own  invention,  and 
he  had  the  benefit  of  accurate  observations  of  the  plftnets 
made  by  Ttcho  Brahb.  The  opportunity  for  determin- 
ing the  true  laws  of  the  motions  of  the  planets  existed  then 
as  it  never  had  before;  and  fortunately  he  was  able, 
through  labors  of  which  it  is  difficult  to  form  an  idea  to- 
day, to  reach  a  true  solution. 

The  Periodic  Time  of  a  Planet.— The  time  of  revolntion 
of  a  planet  in  its  orbit  round  the  3un  (its  periodic  tinu) 
can  be  learned  by  continnons  observations  of  the  planet's 
course  among  the  stars. 


Tan  PLANETARY  MOTIONS. 


106 


hat  of  Kep- 
Bstion  of  the 
Dhti  circular 
d  a  complex 
he  observed 
I  in  accuracy 
ced  into  thb 
bserved.  In 
'or  BO  manj 
the  planets) 
y  difficulties 
>ted. 

[OV. 

I.  1630)  was 
;h  acquaint* 
thorough  be- 
lean  system, 
and  not  the 
i  at  the  same 
>  observe  the 
vention,  and 

the  plftneti 
)r  determin- 
existed  then 
e  was    able, 

an  idea  to- 

»f  revolution 

wiodic  time) 

the  planet's 


From  ancient  times  the  geocentric  positions  of  the 
planets  had  been  observed.  Those  positions  were  referred 
to  the  places  of  the  brightest  fixed  stars,  and  the  relative 
places  of  these  stars  had  been  fixed  with  a  tolerable  ac- 
curacy. The  time  required  for  a  planet  to  move  from  one 
star  to  the  same  star  again  was  the  time  of  revolution  of 
the  planet  referred  to  the  earth. 

The  real  motion  of  the  earth  was  known  from  observa- 
tions of  the  apparent  motion  of  the  sun.  By  calculation 
it  was  possible  to  refer  the  motions  as  observed  (i.e.,  with 
reference  to  the  earth)  to  the  real  motions  (t.0.,  those  about 
the  sun). 

It  was  thus  found  that  the  periodic  times  of  the  known 
planets  were: 


jr<re«ry  about      88  d 

•y 

Vmu»         "       225 

II 

Earth         "       865 

i< 

Mart          "       687 

It 

JvpOer       "     4888 

i< 

Batum       "  10.760 

II 

These  values  were  known  to  the  predecessors  of  Gopeb- 
K10U8.  He  also  showed  (what  is  evident  when  we  examine 
Fig.  34)  that  to  an  observer  on  the  sun  the  motions  of 
the  planets  would  be  always  direct,  and  that  no  stations  or 
retrogradations  of  the  planets  would  be  seen  from  the  sun. 

In  Fig.  36  let  iSbe  the  sun,  E  the  earth,  and  Mn  planet. 
Suppose  the  lines  SB  and  8M  drawn.  They  will  meet 
the  celestial  sphere  at  points  whose  positions  with  refer- 
ence to  the  fixed  stars  could  be  ascertained  by  obser- 
vation. The  relative  positions  of  these  fixed  stars  were 
also  known  by  previous  ol)servations.  The  angle  E'SE* 
was  thus  known  since  it  was  determined  by  the  angular 


I   I 


106 


AsritoxoMr. 


distance  of  the  stars  supposed  to  bo  at  E'  and  J?".  Th« 
•ngleif /;,S'  was  known,  since  it  could  bo  directly  measured 
(the  elongation  of  M  from  the  sun).  Ilonce  the  other  angle 
of  the  triangle  M SK  wns  known,  since  it  was  180"  less  the 
Bum  of  ars  A"'  and  ,S'  E  M.  Thcroforo  a  triangle  could  bo 
conatruiied  which  should  have  the  same  sha))e  as  M E S, 
In  suoh  a  triangle  SM  would  represent  the  distonce  of  the 


ito.aai 


planet  from  the  itrn,  and  8E  the  distance  of  the  earth. 

fi  M 

The  ratio  -^^  could  then  be  determined.    Nothing  was 

known,  from  this  calculation,  of  the  absolute  value  ol  8B 
or  SM'm  miles,  but  observations  of  this  sort  on  all  the 
planets  gave  the  value  of  their  distances  from  the  snn  in 
terms  of  the  distance  of  the  earth  from  the  sun.  It  is 
often  convenient  to  call  the  distance  /S'JP  unity;  and  if  8E 
be  taken  as  the  astronomical  unit,  it  has  been  found  that 


Tim  PLANKrARY  MOTIONS. 


107 


id  J?".  The 
!tly  mouBured 
10  otiicr  angle 
180"  IcflH  tiie 
iglo  could  bo 
1)0  as  MES. 
Htnnce  of  the 


Vot  Mtrtury  (li      0  3871 
Vtnui      <i,  =  0.  .283 


'  the  earth. 

!i^othing  was 

mlm  ot  SB 

'  on  all  the 

the  Ban  in 

sun.    It  1*8 

;  and  if  8E 

foand  that 


Kurth 

II  > 

=  1.0000 

Man 

«. 

1.6887 

Jupiter 

a. 

=  5  ioas 

Saturn 

a. 

=  9.58«^ 

The  cftlcultttion  which  wo  Imve  described  could  be  made 
for  every  poaition  of  ouch  planet,  and  tlius  ita  distances  from 
tlio  sun  ut  every  point  of  its  orbit  could  be  determined. 

The  radim-vector  of  a  planet  is  the  line  which  joins  it  to 
the  sun. 

The  relative  lengths  of  the  radii-veotorea  of  each  pinnet 
at  any  time  were  thus  found  by  observation,  in  terms  of 
the  eurth'H  radias«vector  =  1. 


Fra.  S7. 


Suppose  iS^to  be  the  sun,  and  draw  lines  SP,  SP^,  SP,, 
SP,,  etc.,  to  the  heliocentric  positions  of  a  planet  at  dif- 
ferent times.  On  these  lines  lay  off  distances  5  P,  iSP,, 
SP,,  etc.,  proportional  to  the  lengths  of  the  planet's  radii- 
vectores  determined  as  above.  Join  the  points  P,  P„  P„ 
P„  etc.    The  line  joining  these  is  a  visible  representation 


rliliiilWfifflriTillltWIiillW^ 


^' 


j3^' 


108 


astboMmt. 


t!. 

9   ! 


of  the  shape  of  the  planet's  orbit,  drawn  to  scale.  This 
shape  is  not  that  of  a  circle,  but  it  is  an  ellipse,  and  the 
sun,  S,  is  not  at  the  centre  but  at  a/ociis  of  the  ellipse. 

An  ellipse  is  a  curve  such  that  the  sum  of  the  distances 
of  every  point  of  the  curve  from  two  fixed  points  (the  foci) 
it  a  constant  quantity. 


ria  as. 

Th»  W3ltm.—A  i)  C  P  is  an  elllpM ;  5  and  5*  are  the  fed.  By  the 
definition  of  an  tiWpetSP+Pff^AO,  and  this  is  true  for  ereiy 
point.  8  is  the  focus  occupied  by  the  sun,  "  the  filled  focus."  A  8 
is  the  leait  dittatux  of  the  planet  from  the  sun,  its  perihelion  dutanee; 
and  .4  is  the  periheUon,  that  point  nearest  the  sun.  C  is  the  aphelion, 
the  point  farthest  from  the  sun.  8 A,  SD,  80,  SB,  8P  are  ladii- 
▼ectores  at  different  parte  of  the  orbit,  il  C  is  the  major  aiis 
of  the  orbit  =  2a.  This  major  axis  of  the  orbit  is  twice  the  mean 
auanee  of  the  planet  from  the  sun.  a.  BD  is  the  minor  axis,  26. 
The  ratio  of  08U>  OA  is  the  eeeentrieity  of  the  ellipse.  By  the 
definition  of  the  ellipse,  again,  B8-\-  BS'=AO;  mdB8  =  BSs:  a. 
'S^  =  BO*  +  Qfl*.  or  08=  ¥^^'v  and  the  eccentricity  of  the 

ellipse  is  ^=i2L=i*. 
OA         a 

Keplur't  Laws.— By  compatations  baaed  on  the  observa- 
tions  of  Mart  made  by  Tycho  Brahb,  Keplkb  deduced 


>  jun»Miii»niiwewi»"wnii 


■^   iTHMrwggiiw 


n  to  scale.    This 
n  ellipse,  and  the 
of  the  ellipse, 
t  of  the  distances 
i  points  (the  foci) 


re  the  focL  By  the 
lis  is  true  for  ereiy 
I  filled  focus."  A  8 
I  feriluUon  dktanee; 
I.  (7is  theopAettm, 
\  8B,  8P  ftie  radii- 
Cis  tlie  major  axis 
is  twice  the  nuan 
the  minor  uis,  Sb. 
the  ellipse.  By  the 
uidB8  =  BSssa. 
eccentricity  of  the 


1  on  the  observa- 
Keplkb  deduced 


TBS  PLANSTABT  MOTTONS. 


100 


his  first  two  laws  of  motion  in  the  solar  system.  The  first 
law  of  Keplkb  is — 

/.  JSach  planet  moves  around  the  sun  in  an  ellipse,  hav- 
ing the  sun  at  one  of  its  foci.   To  understand  Law  II: 

Suppose  the  planet  to  be  at  the  points  P,  P„  P„  P„  P^, 
etc.,  at  the  times  T,  T„  T,,  T^,  T^,  etc.   (Fig.  37). 

Suppose  the  times  T,-  T,  T,-  T,,  T,-  T^  to  be  equal. 
Eepleb  computed  the  areas  of  the  surfaces  P  SP^,  P,  8  P„ 
P^iS^Pj  and  found  that  these  areas  were  equal  also,  and 
that  this  was  true  for  each  planet.  The  second  law  of  Ebf- 
LEK  is — 

//.  The  radius-vector  of  each  planet  describes  equal  areas 
inr  equal  times. 

These  two  laws  are  true  for  each  planet  moving  in  its 
own  ellipse  about  the  sun. 

For  a  long  time  Kepler  sought  for  some  law  which 
should  connect  the  motion  of  one  planet  in  its  ellipse  with 
the  motion  of  another  planet  in  its  ellipse.  Finally  he 
found  such  a  irelation  between  the  mean  distances  of  the 
different  planets  (see  table  on  page  107)  and  their  periodic 
times  (see  table  on  p.  106). 

His  third  law  is: 

///.  The  squares  of  the  periodic  times  of  the  planets  are 
proportional  to  the  cubes  of  their  mean  distances  from  the 
sun. 

That  is,  if  7*,,  T,,  T,,  etc.,  are  the  periodic  times  of  the 
different  planets  whose  mean  distances  are  a„  a„  a„  etc., 
then 


I*' 


T*:  T;-a,* 
T*  :  T*  =  o/  :  a/; 
etc.  etc. 


4\ 


iipMsiiiRP' 


4 


110 


AsTitoyoMr. 


If  T^  and  ^  M«  the  periodic  time  and  the  mean  distance 
of  the  earth,  and  if  T,  (=  1  year)  is  taken  as  the  unit  of 
time  and  a,  as  the  unit  of  distance,  then  we  shall  have 

r.'  :  1  =  a.*  :  1  or  ^*  =  1  or  -^  =  1; 

7'-l  =  a-lor^  =  lor||  =  l; 

and  so  on. 

The  data  which  Kepler  had  were  not  quite  so  accurate 
as  those  which  we  have  given,  and  the  table  below  shows 
the  very  figures  on  which  Eepleb's  conclunon  was  based: 

Mercury 0.2878  0.2408yean  1.018 

FeniM 0.6104             0.6151  1.008 

JBarlh l.OOdO            1.0000  1.000 

Mar$. 1.8740             1.8810  1.004 

JvpOer 11.014  11.8764  0.986 

BatHrn 88.058  20.4605  1.060 

Although  the  numbers  in  the  third  column  were  not 
strictly  the  same,  their  differences  were  no  greater  than 
might  easily  have  been  produced  by  the  errors  of  the  obsw- 
yations  which  Kepler  used;  and  on  the  evidence  here 
given  he  advanced  his  third  law.  The  order  of  discovery 
of  the  true  theory  of  the  solar  system  was,  then — 
I.  To  prove  that  the  earth  moved  in  space; 
II.  To  prove  that  the  centre  of  this  motion  was  the  sun; 

III.  To  establish  the  three  laws  oi  Kepler,  which  gave 
the  circumstances  of  this  motion.  „ 

By  means  of  the  first  two  laws  of  Kepuek  the  motions  of  eadi 
planet  in  ite  own  ellipse  became  known;  that  is.  the  poaition  of  the 
planet  at  any  future  time  could  be  predicted.  For  example,  if  the 
planet  was  at  P  at  a  time  7,  and  the  question  was  as  to  ita  place  at  • 
subsequent  time  T.  this  could  be  solved  by  compuUng,  first,  how 


i 

mi 


sanaMaakw 


mtmtitmmm 


;he  mean  distance 
m  as  the  unit  of 
ire  shall  have 


1; 


T 


)aite  so  accurate 
able  below  shows 
UMon  was  based: 


18  years 

SI 

(0 

[0 

\i 

» 


1.018 
1.008 
1.000 
1.004 
0.990 
l.OSO 


iolumn  were  not 
no  greater  than 
Tors  of  the  obsmr- 
lie  evidence  here 
rder  of  discoTery 
,  then — 
space; 

>tiunwa8the8an; 
'LEB,  which  gave 


he  motions  of  eadi 
,  the  position  of  the 
For  example,  if  the 
is  as  to  its  place  at  • 
imputing,  first,  how 


TEE  PLAjmfAHF  MOTIONS. 


in 


large  an  area  woidd  be  described  by  the  radius-vector  in  the  interval 

T  —  T;  and  second,  what  the  angle  at  8  of  the  sector  having  this 

area  would  be.    Then  drawing  a  line  tlirough  8  making  this  angle 

with  the  line  SP(8ay  8P,),  atd  laying  off  the  length  of  the  ladiufc 

Tcctor  SP„  the  position  of  the  planet  iKcame  known. 

From  the  third  law  the  relative  values  of  tlie  mean  distancea 

di,  oi,  flt,  at,  etc..  could  be  determined  with  great  and  increasing  ac 

curacy. 

T 
From  the  equation—  =  1,  a  could  be  determined  so  soon  as  Twas 
^  ai 

known.    With  each  revolution  of  the  planet  T  became  known  more 

accurately,  as  did  also  a. 

These  laws  are  the  foundations  of  our  present  theory  of  the  solar 
system.  They  were  based  on  observation  pure  and  simple.  We  may 
anticipate  a  little  to  say  that  these  laws  have  been  compared  with 
the  most  precise  ol>servations  we  can  make  at  the  present  time,  and 
discussed  iu  all  their  consequences  by  processes  unknown  to  Kep- 
ler, aud  that  they  are  strictly  true  if  we  make  the  following  modifl- 
cations. 

If  there  were  only  one  planet  revolving  alxnit  tlie  sun,  then  it 
would  revolve  in  a  perfect  ellipse,  and  ol)ey  the  second  law  exactly. 
In  a  system  composed  of  the  sun  and  more  than  one  planet  each 
planet  disturbs  the  motion  of  every  other  slightly,  by  attraotiag  it 
from  the  orbit  which  it  would  otlierwise  follow. 

Thus  neither  the  first  nor  the  second  law  can  be  precisely  true  of 
any  planet,  although  they  are  very  nearly  so.  In  the  same  way  the 
relation  lietwoen  the  orbits  of  any  two  planets  as  expressed  in  the 
third  law  in  not  prfetM,  nlli^ough  it  is  a  very  close  approximation. 

Xlementt  of  a  Planet's  Orbit.— Wlien  we  know  a  and  b  for  any  orbit, 
the  shape  and  size  of  tlie  orbit  is  known. 

Knowing  a  we  alsd  know  T,  the  periodic  time;  in  fact  a  is  found 
from  7  by  Keflbr's  law  III. 

If  wo  know  the  planet's  celestial  longitude  (L)  at  a  given  epoch, 
say  December  81st.  1850,  we  have  all  the  Oementt  necessary  for 
finding  the  place  of  the  planet  in  it$  orftU  at  any  time,  as  has  been 
explained  (page  110). 

The  orbit  lies  in  a  certain  plane;  this  plane  intersects  the  plane  of 
the  ecliptic  at  a  certain  angle,  which  we  call  the  intUnation  i.  Know- 
ing I,  the  plane  of  the  planet's  orbit  is  fixed.  The  plane  of  the 
orbit  intersects  the  plane  of  the  ecliptic  in  a  line,  the  line  <ffthenode$. 
Half  of  the  planet's  orbit  lies  below  (south  oO  the  plane  of  the 
ecliptic  and  half  above.  As  tlie  planet  moves  in  iU  orbit  it  must 
pHS  through  tlie  plane  of  the  ecliptic  twice  for  every  revolutioB, 


119 


ASTRONOMT. 


I  I 


The  point  where  it  passes  througli  the  ecliptic  going  from  the  south 
half  to  the  north  lialf  of  ito  orbit  is  the  ateending  node;  the  point 
wliere  it  passes  through  the  ecliptic  going  from  nortli  to  south  is 
the  deaeending  node  of  the  planet's  orbit.  If  we  have  only  the  in- 
elination  given,  the  orbit  of  tlie  planet  may  lie  anywhere  in  the  plane 
whose  angle  with  the  ecliptic  is  i.  If  we  fix  the  place  of  the  nodes 
or  of  oae  of  them,  the  orbit  i<i  thus  fixed  in  its  plane.  This  we  do 
by  giving  the  (celestial)  longitude  of  the  ascending  node  A. 

Now  everything  is  known  except  the  relation  of  the  planet's  orbit 
to  the  sun.    This  is  fixed  by  the  longitude  of  the  perihelion,  or  P. 
Thus  the  tfefiMnto  of  a  planet's  orbit  are: 

i",  the  indination  to  the  ecliptic,  which  fixes  tlie  plane  of  the  planet's 
orbit; 

a,  the  longitude  of  the  node,  which  fixes  the  position  of  the  line  of 
interseniion  of  the  orbit  and  the  ecliptic; 

P,  the  longitude  of  the  perihelion,  which  fixes  the  position  of  the 
msjor  axis  of  the  planet's  orbit  with  relation  to  the  sun,  and  hence 
in  space; 

a  and  e,  the  mean  dietanee  and  eeeentrieitjf  of  the  orbit,  which  fix 
the  shape  and  size  of  the  orbit; 

I  and  M,  the  periodie  time  and  the  longitude  at  epoch,  which  enable 
the  place  oT  the  planet  in  its  orbit,  and  hence  in  space,  to  be  fixed  at 
any  future  or  past  time. 

The  elements  of  the  older  planeU  of  the  solar  system  are  now 
known,  with  great  accuracy,  and  their  positions  for  two  or  three  cen- 
turies past  or  future  can  be  preduOed  with  a  clos^  approximation  to  the 
accuracy  witli  which  these  positions  can  be  observed. 


■    •■   /.:j»   r.'.,,>  :■'•'  ,■-  j^i.i',    u^W 

,...      •  -vji' :.«..:;.•_   \.  ;.  .v.'*.'. 


ng  from  the  south 
ng  node;  the  point 
north  to  south  is 
have  only  the  tn. 
where  in  the  plane 
lace  of  the  nodes, 
ilane.  This  we  do 
node  A. 

'  tlie  planet's  orbit 
rihdion,  or  P. 

lane  of  the  planet's 

lion  of  the  line  of 

le  position  of  tlio 
le  sun,  and  hence 

B  orbit,  which  fix 

oeA,  whicli  enable 
ace,  to  be  fixed  at 

'  system  are  now 
two  or  three  cen- 
>roximation  to  the 
id. 


.     .       ,.-..■'; 


^.»^Ul*^^;  ■»■.;.  ■*v)V;'fft.'*\^ 


CHAPTER  VI. 
UNIVERSAL    GRAVITATION. 

HXWTOH'S  LAWB  07  KOTIOV 

The  ceiablishmcnt  of  the  theory  of  universal  gravitation 
furnishes  one  of  the  best  examples  of  scientific  method 
which  is  to  be  found.  We  shall  describe  its  leading  features, 
less  for  the  purpose  of  making  known  to  the  reader  the 
technical  nature  of  the  process  than  for  illustrating  the 
true  theory  of  scientific  investigation,  and  showing  that  such 
investigation  has  for  its  object  the  discovery  of  what  we 
may  call  generalized  facts.  The  real  test  of  progress  ia 
found  in  our  constantly  increased  ability  to  foresee  either 
the  course  of  nature  or  the  effects  of  any  accidental  or  arti- 
ficial combination  of  causes.  So  long  as  prediction  is  not 
possible,  the  desires  of  the  investigator  remain  unsatisfied. 
When  certainty  of  prediction  is  once  attained,  and  the 
laws  on  vhich  the  prediction  is  founded  are  stated  in  their 
simplest  form,  the  work  of  science  is  complete. 

To  the  pre-Newionian  astronomers  the  phenomena  of 
the  geometrical  htws  of  planetary  motion,  which  we  have 
just  described,  formed  a  group  of  facts  having  no  connection 
with  anything  on  the  earth's  surface.  The  epicycles  of 
HipPARCHUS  and  Ptolemy  were  a  truly  scientific  concep- 
tion, in  that  they  explained  the  seemingly  erratic  motions 
of  the  planets  by  «  wngl?  aimple  ]|tw,    In  the  heliocentric 


sX 


W&m 


»wiMilSIH 


Nil 


114 


ASTRONOMY. 


i     : 
.1 


theory  of  Oopbrnicus  this  law  was  still  further  simplified 
by  dispensing  in  great  part  with  the  epicycle,  and  replacing 
the  latter  by  a  motion  of  the  earth  around  the  sun,  of  the 
same  nature  with  the  motions  of  the  planets.  But  Coper- 
nicus had  no  way  of  accounting  for,  or  even  of  describing 
with  rigorous  accuracy,  the  small  deviations  in  the  motions 
of  the  planets  around  the  sun.  In  this  respect  he  made  no 
real  advance  upon  the  ideas  of  the  ancients. 

Kepleb,  in  his  discoveries,  made  a  great  advance  in  rep- 
resenting the  motions  of  all  the  planets  by  a  single  set  of 
simple  and  easily  understood  geometrical  laws.  Had  the 
planets  followed  his  laws  exactly,  the  theory  of  planetary 
motion  would  have  been  substantially  complete.  Still, 
farther  progress  was  desired  for  two  reasons.  In  the  first 
place,  the  laws  of  Kepler  did  not  perfectly  represent  all 
the  planetary  motions.  When  observations  of  the  greatest 
accuracy  were  made,  it  was  found  that  the  planets  deviated 
by  small  amounts  from  the  ellipse  of  Kepler.  Some  small 
emendations  to  the  motions  computed  on  the  elliptic  theory 
were  therefore  necessary.  Had  this  requirement  been  ful- 
filled, still  another  step  would  have  been  desirable;  namely, 
that  of  connecting  the  motions  of  the  planets  with  motions 
upon  the  earth,  and  reducing  them  to  the  same  laws. 

Notwithstanding  the  great  step  which  Kepler  made  in 
describing  the  celestial  motions,  he  unveiled  none  of  the 
■  great  mystery  in  which  they  were  enshrouded.  When  Kep< 
LBB  said  that  observation  showed  the  law  of  planetary  mo- 
tion to  be  that  around  the  circumference  of  an  ellipse,  as 
asserted  in  his  law,  he  said  all  that  it  seemed  possible  to 
learn,  supposing  the  statement  perfectly  exact.  And  it 
was  all  that  conld  be  learned  from  the  mere  study  of  the 
l)laaetar7'  motions.    In  order  to  connect  these  motions  with 


VrnVKHSAL  QUA  VlTAl'ION. 


116 


■ther  simplified 
,  and  replacing 
the  sun,  of  the 

.      But  COPER- 

n  of  describing 
in  the  motions 
Bct  he  made  no 

advance  in  rep- 
a  single  set  of 
iws.  Had  the 
•y  of  planetary 
mplete.  Still, 
In  the  first 
jr  represent  all 
of  the  greatest 
lanets  deviated 
\.  Some  small 
I  elliptic  theory 
nent  been  ful- 
rable;  namely, 
s  with  motions 
me  laws. 
PLER  made  in 
li  none  of  the 
.  When  Kep. 
planetary  mo- 
\  an  ellipse,  as 
ed  possible  to 
xact.  And  it 
3  study  of  the 
B  motions  with 


those  on  the  earth,  the  next  step  was  to  study  the  laws  of 
force  and  motion  here  around  us.  Singular  though  it  may 
appear,  the  ideas  of  the  ancients  on  this  subject  were  far 
more  erroneous  than  their  conceptions  of  the  motions  of 
the  planets.  We  might  almost  say  that  before  the  time  of 
Galileo  scarcely  a  single  correct  idea  of  the  laws  of  motion 
was  generally  entertained  by  men  of  learning.  Among 
those  who,  before  the  time  of  Xewtok,  prepared  the  way 
for  the  theory  in  question,  Galileo,  Huyohens,  and 
HooKE  are  entitled  to  especial  mention.  The  general  laws 
of  motion  laid  down  by  Newton  were  three  in  number. 

Law  Firfct:  Every  body  preserves  its  state  of  rest  or  of 
uniform  motion  in  a  right  line,  unless  it  is  compelled  to 
change  ffutt  state  by  forces  impressed  thereon. 


.  It  was  formerly  supposed  tbnt  a  body  acted  on  by  no  force  tended 
to  come  to  rest.  Here  lay  one  of  tbe  greatest  difiicullies  wbicb  the 
predecessors  of  Nbwtoii  found,  in  accounting  for  the  motion  of  the 
planets.  Tbe  idea  tbat  the  sun  in  some  way  caused  these  motions 
waa  entertained  from  the  earliest  times.  Even  ProLEifTluula  vagw 
idea  of  a  force  which  was  always  directed  toward  the  centre  of  the 
earth,  or,  wbidi  waa  to  him  tbe  same  thing,  toward  tbe  centra  of  th« 
universe,  and  which  not  only  caused  heavy  bodies  to  fall,  but  bound 
the  whole  universe  togetlier.  KsriJn,  again,  distinctly  affirms  the 
existence  of  a  gravitating  force  by  whicli  the  sun  acts  on  the  planeU; 
but  he  supposed  that  the  sun  must  also  exercise  an  impulsive  forward 
force  to  lieep  the  pl«nets  in  motion.  Tbe  reason  of  thb  incorrect 
idea  was,  of  course,  tbat  all  bodies  in  motion  on  the  surface  of  the 
earth  had  practically  come  to  rest.  But  what  was  not  clearly  seen 
befora  the  time  of  Nbwtoh,  or  at  least  before  Oaulbo,  waa  that 
this  arose  from  the  inevitable  resisting  forces  which  act  upon  all 
moving  bodies  upon  tbe  earth. 


Law  Second:  The  alteration  of  motion  i*  wer  propor- 
tional to  the  moving  force  impressed,  and  i$  made  in  thi 
dir^ittn  of  the  right  line  in  wAiVA  thot/afee  #«||, 


m 


..ii'iTii«gi«Biiwiw^ 


MiiW' 


116 


ASTJtONOMT. 


The  first  law  might  be  conaidered  m  a  particular  caae  of  thii  seo- 
ond  one  wliich  arises  wlien  the  force  is  supposed  to  vanish.  The  ac- 
curacy of  botli  laws  can  be  proved  only  by  very  carefully  conducted 
experiments.    They  are  now  considered  as  conclusively  proved. 

Law  Third:  To  every  action  there  ia  always  opposed  an 
equal  reaction  ;  or  the  mutual  actions  of  two  bodies  upon 
each  other  are  always  equal,  and  in  opposite  directions. 

Tliat  is,  if  a  body  A  acts  in  any  way  upon  a  body  B,  B  will  exert 
a  force  exnctly  equal  on  A  in  the  opposite  direction. 

These  laws  once  established,  it  became  possible  to  eofeulato  the  mo- 
tion of  any  body  or  system  of  bodies  when  once  the  forces  which  act 
on  them  were  known,  and,  tie*  ttrta,  to  define  what  forces  were  re- 
quisite to  produce  any  given  motion.  The  question  which  presented 
itself  to  the  mind  of  Newton  and  his  contemporaries  was  this:  Under 
vhat  lav  of  force  teill  planets  mote  round  the  ran  in  aeeordanee  with 
KkPlbb's  lawe  t 

Supposing  a  body  to  move  around  in  a  circle,  and  putting  B  the 
mdius  of  tlie  circle,  T  the  period  of  revolution,  HuvoHENshad  shown 
that  the  centrifugal  force  of  the  body,  or,  which  is  the  same  thing, 
the  attractive  force  toward  the  centre  which  would  keep  it  in  the 

dlole.  was  proportional  to  -=r  But  by  Krpler'b  third  law  7*  is  pro- 
portional to  Bf.  Therefore  this  centripetal  force  is  proportional  to 
-^:  that  is,  to-^.    Thus  it  followed  immediately  from  KEPUtR'i 

third  law  that  tlie  central  force  which  would  keep  the  planeU  in  their 
orbits  was  inversely  as  the  square  of  the  distance  from  the  sun,  sup- 
posing each  orbit  to  be  circular.  The  first  law  of  motion  once  com- 
pletely understood,  it  was  evident  that  the  planet  needed  no  force 
impelling  it  forward  (o  keep  up  iu  motion,  but  that,  once  started,  it 
would  keep  on  forever. 

The  next  step  was  to  solve  the  problem.  What  law  of  force  will 
make  a  planet  describe  an  ellipse  around  the  sun.  having  the  latter 
in  one  of  its  foci?  Or,  supposing  a  planet  to  move  round  the  sun, 
the  latter  attracting  it  with  a  force  inversely  as  the  square  of  the  dto- 
tance;  what  will  be  the  form  of  the  orbit  of  the  planet  if  it  is  not  cir- 
cular? A  solution  of  either  of  these  problems  was  beyond  the  power 
of  mathematicfauM  before  the  time  of  Newtos;  and  it  thus  remained 
uncertain  whether  the  planeu  moving  under  the  Influence  of  the 
«un's  gravitation  would  or  would  not  deapribe  eUlfMea.    VoaUe,  «| 


CAM  of  thU  see- 

vanith.  The  to- 
■nfully  conducted 
irely  proTed. 

iy«  opposed  an 
vo  bodies  upon 
direcliona. 

yB,B  will  exert 
I. 

oaUeukUeibtmO' 
9  foroea  which  set 
It  forces  were  re- 
I  which  presented 
iwasthia:  Vhdtr 
n  aeeordanet  with 

nd  putting  H  the 

OHENB  had  shown 

the  same  thing. 

Id  keep  it  in  the 

bird  law  7*  is  pro- 
is  proportional  to 
Y  from  Kepucr's 

be  planets  in  their 
■om  the  sun,  sup- 
notion  once  oom- 
needed  no  force 
t,  once  started,  it 

law  of  force  will 
haying  the  latter 
B  round  the  sun, 
square  of  the  die- 
Met  if  It  is  not  cir- 
bejrond  the  power 
1  it  thus  remained 
I  Inlluenoe  of  the 
Ipeea.    Vb>U*i  M 


UmVSRaAL  ORAVlTATIOy. 


117 


first,  to  reach  a  satisfactory  solution,  Newtom  attacked  the  problem 
in  another  direction,  sUrting  from  llie  gravitation,  not  of  the  sun, 
but  of  the  earth,  as  explained  in  the  following  section. 

OBATXTAnov  nr  not  ExAYura 

The  reader  is  probably  familiar  with  the  story  of  New- 
ton and  the  falling  apple.    Although  it  has  no  anthorita- 
tiye  foundation,  it  is  strikingly  illustrative  of  the  method 
by  which  Nbwtok  must  have  reached  a  solution  of  the 
problem.    The  course  of  reasoning  by  which  he  ascended 
from  gravitation  on  the  earth  to  the  celestial  motions  was  as 
follows:  We  see  that  there  is  a  force  acting  all  over  the  earth 
by  which  all  bodies  are  drawn  toward  its  centre.    This 
force  is  called  gravitation.    It  extends  without  sensible 
diminution  to  the  tops  not  only  of  the  highest  buildings, 
but  of  the  highest  mountains.    How  much  higher  does  it 
extend?    Why  should  it  not  extend  to  the  moon?    If  it 
does,  the  moon  would  tend  to  drop  toward  the  earth,  just 
as  a  stone  thrown  from  the  hand  drops.    As  the  moon 
moves  round  the  earth  in  her  monthly  course,  there  must 
be  some  force  drawing  her  toward  the  earth;  else,  by  the 
first  law  of  motion,  she  would  fly  entirely  away  in  a  straight 
line.    Why  should  not  the  force  which  makes  the  apple 
fall  be  the  same  force  which  keeps  her  in  her  orbit?    To 
answer  this  quetition,  it  was  not  only  necessary  to  calculate 
the  intensity  of  the  force  which  would  keep  the  moon  her- 
self in  her  orbit,  but  to  compare  it  with  the  intensity  of 
gravity  at  the  earth's  surface.    It  had  long  been  known 
that  the  distance  of  the  moon  was  about  sixty  ndii  of  the 
earth,  from  measures  of  her  parallax  (see  page  67).    If 
this  force  diminished  as  the  inverse  square  of  the  distance, 
thea  «t  the  moon  it  woald  be  only  j^^  as  great  as  at  the 


M-lfrHrWTftMaii 


118 


ASTRONOMY. 


surface  of  the  earth.  On  the  earth  a  body  falls  sixteen  feet 
in  a  second.  If,  then,  the  theory  of  gravitation  were  cor* 
rect,  the  moon  ought  to  full  towards  the  earth  3,^7  °^  ^^'' 
amount,  or  about  -^  of  an  inch  in  a  second.  The  moon 
being  in  motion,  if  we  imagine  it  moving  in  a  straight  line 
at  the  beginning  of  any  second,  it  ought  to  be  drawn  away 
from  that  lino  ^  of  an  inch  at  the  end  of  the  second. 
When  the  calculation  was  made  it  was  found  to  agree  ex- 
actly with  this  result  of  theory.  Thus  it  was  shown  that 
the  force  which  holds  the  moon  in  her  orbit  is  the  same 
force  that  makes  the  stone  fall,  diminished  as  the  inverse 
square  of  the  distance  from  the  centre  of  the  earth. 

It  thus  appeared  that  central  forces,  both  toward  the  sun 
and  toward  the  earth,  varied  inversely  as  the  squares  of  the 
distances.  Kepler's  second  law  showed  that  the  line  urawn 
from  the  planet  to  the  sun  would  describe  equal  arcus  in 
equal  times.  Newtox  showed  that  this  could  not  be  true 
unless  the  force,  which  held  the  planet  was  directed  toward 
the  sun.  Wo  have  already  stated  that  the  third  law  showed 
that  the  force  was  inversely  as  the  square  of  the  distance, 
and  thus  agreed  exactly  with  the  theory  of  gravitation.  It 
only  remained  to  consider  the  resultf  of  the  first  law,  that 
of  the  elliptic  motion.  After  long  utA  laborious  efforts, 
Newtok  wus  enaoled  to  demonstrate  rigorously  that  this 
law  also  resulted  from  the  law  of  the  inverse  square,  and 
could  result  from  no  other.  Thus  all  mystery  disappeared 
from  the  celestial  motions;  and  planets  were  shown  to  be 
simply  heavy  bodies  moving  according  to  the  same  laws  that 
were  acting  here  around  us,  only  under  very  different  cir- 
cumstances. All  three  of  Keplbb's  laws  were  embraced  in 
the  single  law  of  gravitatian  toward  the  sun.  The  sun  at- 
tracts the  planets  as  the  «arth  attracts  bodies  here  »roand  w^ 


'  #)»  (4-. '«  ^  ^ 


UNIVERSAL  GRAVJTATJOK. 


lift 


8  sixteen  feet 
ion  wore  cor- 
*>  siVt  ot  this 
The  moon 
straight  liiio 
druwn  nway 
f  the  second, 
to  agree  ex- 
s  shown  that 
.  is  the  same 
IS  the  inverse 
earth. 

)wurd  the  snn 
squares  of  the 
.hclineurawn 
qual  areus  in 
Id  not  l>e  true 
rectcd  toward 
d  law  showed 
the  distance, 
Eivitation.    It 
irst  law,  that 
rioQs  efforts, 
nslythat  this 
)  square,  and 
f  disappeared 
shown  to  be 
one  laws  that 
different  oir« 
embraced  in 
The  sun  at- 
re»roandlw« 


K«tul  AotlftB  of  tk«  71«MU.—ny  NRWTOM'stlilnl  law  of  motion, 
cacli  pluiiet  mu8t  nltrnrt  the  lun  with  n  force  equnl  to  that  which  the 
nun  exertH  upon  the  planet.  The  moou  nloo  must  attract  the  earth 
as  nuich  ns  the  earth  attracts  the  moon.  Sucli  being  the  case,  it 
must  l>e  highly  probable  that  the  planets  attract  each  other.  If  so, 
Keplkk'h  laws  can  only  be  an  approximation  to  the  trutli.  The  sun, 
Itoing  imineniwly  more  massive  than  any  of  tlie  planets,  overpowers 
their  attraction  upon  each  other,  and  makes  the  law  of  elliptic  mo- 
tion very  nearly  true.  But  still  the  comparatively  small  attraction 
of  the  planets  must  cause  some  deviations.  Now,  deviations  from 
the  pure  elliptic  motion  were  known  to  exist  in  the  case  of  several  of 
the  planets,  notably  in  that  of  the  moon,  which,  if  gravitation  were 
universal,  must  move  under  the  influence  of  the  combined  attraction 
of  the  enrih  and  of  llie  sun.  Newton,  therefore,  attacked  the  com- 
plicated  problem  of  the  determination  of  the  motion  of  the  moon 
under  tiie  combined  action  of  these  two  forces.  He  showed  in  a 
general  way  that  its  deviations  would  \te  of  the  same  nature  as  those 
shown  by  observation.  But  the  complete  solution  of  the  problem, 
whicli  required  the  answer  to  be  expressed  in  numbere,  was  beyond 
his  power. 

OntTitation  Reiidet  in  each  Particle  of  Katter.— Still 
another  question  arose.  Were  these  mutually  attractive 
forces  resident  in  the  centres  of  the  several  bodies  attracted, 
or  in  each  particle  of  the  matter  composing  them?  Nsw- 
TOK  showed  that  the  latter  must  be  the  case,  because  the 
smallest  bodies,  as  well  as  the  largest,  tended  to  fall  toward 
the  earth,  thns  showing  an  eqnal  gravitation  in  every  sepa- 
rate part.  It  was  also  shown  by  Newton  that  if  a  planet 
were  on  the  snrface  of  the  earth  or  outside  of  it,  it  woald 
be  attracted  with  the  same  force  as  if  the  whole  mass 
of  the  earth  were  concentrated  in  its  centre.  Putting 
together  the  various  results  thus  arrived  at,  Nswroir 
was  able  to  formnlate  his  great  law  of  universal  gravita- 
i^on  in  these  comprehensive  wot6b:  "  Fverp .  particle  of 
matter  in  the  universe  attracte  every  other  particle  with 
a  force  directly  at  the  maetes  of  the  two  partielet,  and 


?fSESP?S«»i; 


1^""     -    ,.   .-I^^^i^, 


Vi&iHtiiiiUlSJ 


^si^^^ss^s^ms^s^sss^S^SSSS^ 


120 


ASTRONOMY. 


\nver$ely  at  the  tquart  of  the  distance  which  separate* 
them:* 

To  ihow  the  nature  of  the  attractive  force*  among  theM  Tarioua 
particle*,  let  us  represcot  by  m  und  m'  the  mawM  of  two  attracting 
bodies.  We  may  conceive  the  body  m  to  be  compoMd  of  m  par- 
tides,  and  the  otiier  body  to  be  composed  of  m'  particles.  Let  us 
conceive  that  each  particle  of  one  body  attracU  each  particle  of  the 

other  with  a  force  ^.    Then  every  particle  of  m  will  be  attracted  by 

eochof  tiie  m'  particles  of  the  other,  and  therefore  the  total  attractive 

force  on  eacli  of  tlie  m  particles  will  be  -^.    Each  of  tite  m  partlclea 

being  equally  subject  to  this  attraction,  tiie  total  attractive  force  be. 

tween  the  two  bodies  will  bo  ~     When  a  given  force  acts  upon 

a  body,  it  will  produce  less  motion  the  larger  the  bo«ly  is,  tlie  aeeel- 
entHng  force  being  proportional  to  the  total  attracting  force  divided 
by  the  moss  of  the  Inxiy  moved.  Therefore  the  accelerating  force 
whicli  acts  on  tlic  body  m',  and  whidi  determines  tlio  amount  of 

motion,  will  be  ^;  and  conversely  the  accelerating  foree  acting  on 
tiie  body  m  will  be  represented  by  tlie  fraction  — 

&I1IA1W  Oir  TEE  THIOBT  OF  OlATITAnoV. 

The  real  natnre  of  the  great  discovery  of  Newton  is  so 
frequently  misunderstood  that  a  little  attention  may  be 
given  to  its  elucidation.  Gravitation  is  frequently  spoken 
of  ai  if  it  were  a  theory  of  Nbwtow's,  and  very  generally 
received  by  astronomers,  but  still  liable  to  be  ultimately 
rejected  as  a  great  many  other  theories  have  been.  Not 
infrequently  people  of  greater  or  less  intelligence  are  found 
making  great  efforts  to  prove  it  erroneous.  Newtok  did 
not  discover  any  new  force,  but  only  showed  that  the 
motioni  of  the  heavens  could  be  ateounted  for  by  a  force 
which  we  aU  know  to  exist    Grartation  (Latin  ^roi>»W»— 


Meh  separates 


ing  these  rariout 
>t  two  attractiDg 
poMd  of  f>t  par 
larticlea.  Let  ui 
I  particle  of  tlie 

I  be  attracted  by 

e  total  attractive 

if  the  m  partlclet 

iictivo  force  be> 

force  acts  upon 

xly  li,  the  aecel- 

\g  forcu  divided 

«;elcmtiDg  force 

the  amount  of 

force  acting  on 


rAnov. 

^EWTOK  is  80 

ition  may  be 
lently  spoken 
erj  generally 
be  altimately 
B  been.  Not 
nee  are  found 
Nbwtow  did 
red  tbat  the 
For  by  a  force 
in  gravitd*— 


VNl  VERSAl  GkA  VltA  TlOif. 


121 


weight,  heaviness)  is  the  force  which  makes  all  bodies 
here  at  the  surface  of  the  earth  tend  to  fall  downward; 
and  if  any  one  wishes  to  subvert  the  theory  of  gravitation, 
he  must  begin  by  proving  that  this  force  does  not  exist. 
This  no  one  would  think  of  doing.  What  Newton  did 
was  to  show  that  this  force,  which,  before  his  time,  had 
been  recognized  only  as  acting  on  the  surface  of  the  earth, 
really  extended  to  the  heavens,  and  that  it  resided  not  only 
in  the  earth  itself,  but  in  the  heavenly  bodies  also,  and  in 
each  particle  of  matter,  however  situated.  To  put  the 
matter  in  a  terse  form,  what  Newton  discovered  was  not 
gravitation,  but  the  universalitif  of  gravitation. 

It  may  be  inquired,  is  the  induction  which  snpposei 
gravitation  universal  so  complete  as  to  be  entirely  beyond 
doubt?    We  reply  that  within  the  solar  system  it  certainly 
is.     The  laws  of  motion  as  (Bstablished  by  observation  and 
experiment  at  the  surface  of  the  earth  must  be  considered 
as  mathematically  certain.    It  is  an  observed  fact  that  the 
planets  in  their  motions  deviate  from  straight  li:>»  -  in  a 
certain  way.     By  the  first  law  of  motion,  such  de   ation 
'  can  be  produced  only  by  a  force;  and  the  direction  and 
intensity  of  this  forc^  admit  of  being  calculated  once  that 
the  motion  is  determined.    When  thus  calcuUted,  it  is 
found  to  be  exactly  represented  by  one  great  force  con- 
stantly directed  toward  the  sun,  and  smaller  subsidiary 
forces  directed  toward  the  several  planets.    Therefore  no 
fact  in  nature  is  more  firmly  established  than  that  of  uni- 
versal gravitation,  as  hud  down  by  Niwton,  at  least  within 
the  sokr  system. 

We  shall  find,  in  describing  double  stars,  that  gravita- 
tion is  also  found  to  act  between  the  components  of  a  great 
number  of  such  itun.     It  it  certain,  thfrefore,  that  at 


m 


ASrMNdkt. 


If 


■■'■i': 


i': 


least  some  stai^  gravitate  toward  each  other,  as  tl.o  bodies 
of  the  solar  system  do;  but  the  distance  which  separates 
most  of  the  stars  from  each  other  and  from  our  snn  is  so 
immense  that  no  evidence  of  gravitation  between  individual 
stars  and  the  sun  has  yet  been  given  by  observation.  Still, 
that  they  do  gravitate  according  to  Newton's  law  can 
hardly  be  seriously  doubted  by  any  one  who  understands 
the  subject. 

The  student  may  now  be  supposed  to  see  the  absurdity 
of  supposing  that  the  theory  of  gravitation  can  ever  be 
subverted.  It  is  not,  however,  absurd  to  sup))ose  that  it 
may  yet  be  shown  to  be  the  result  of  some  more  general 
law.  Attempts  to  do  this  are  made  from  time  to  time 
by  men  of  a  philosophic  spirit;  but  thus  far  no  theory  of 
the  subject  having  much  probability  in  its  favor  has  been 
propounded. 


iV  »;w**w^i.*i**ii* 


;r,  as  tl.o  bodies 
Krhich  separates 
tm  our  snn  is  so 
nrecn  individoal 
jrvation.  Still, 
ton's  law  can 
tio  understands 

>  the  absurdity 
on  can  ever  be 
suppose  that  it 
)  more  general 
I  time  to  time 
ir  no  theory  of 
favor  has  been 


CHAMEU  Vrt. 

THB  MOTIONS  AND  ATTRACTION  OP  THE  MOON. 

Each  of  the  planets,  except  Merairy  and  Venus,  is  at- 
tended by  one  or  more  satellites,  or  moons  as  they  are 
sometimes  familiarly  called.    These  objects  revoke  around 
their  several  planets  in  nearly  circular  orbits,  accompany- 
ing them  in  their  revolutions  around  the  sun.    Their  dis- 
tances  from  their  planets  are  very  small  compared  with  the 
distances  of  the  latter  from  each  other  and  from  the  sun. 
Their  magnitudes  also  are  very  small  compared  with  those 
of  the  planets  around  which  they  revolve.    Considering 
each  system  by  itself,  the  satellites  revolve  around  their 
central  planets,  or  "primaries,"  in  nearly  circular  orbits, 
and  in  each  system  Kepler'8  laws  govern  the  motion  of  the 
satellites  about  the  primary.    Each  system  is  carried  around 
the  sun  without  any  derangement  of  the  motion  of  its  sev- 
eral bodies  among  themselves. 

Our  earth  has  a  single  satellite  accompanying  it  in  this 
way,  the  moon.  It  revolves  around  the  earth  in  a  little 
less  than  a  month.  The  nature,  causes,  and  consequences 
of  this  motion  form  the  subject  of  the  present  chapter. 

Thx  Moob'8  Monon  Airs  Teamxil 

That  the  moon  performs  a  monthly  circuit  In  the  heavens  Is  a  fact 
with  which  we  are  all  familiar  from  childhood.  At  certain  time*  we 
.eehernewly emerged  from  thetun'a  rays  in  theweatem  twilight, 
and  then  we  call  her  the  now  moon.    On  each  succeeding  evening 


124 


ASTRONOMY. 


we  see  her  further  to  the  east,  so  that  in  two  weeks  she  is  opposit* 
tl  0  sun,  rising  in  the  east  as  he  sets  in  tlie  west.  Continuing  her 
course  two  weeits  more,  slie  has  approached  tlie  sun  on  the  other 
side,  or  from  tiie  west,  and  is  once  more  lost  in  his  rays.  At  the  end 
of  twenty-nine  or  thirty  days,  we  see  her  again  emerging  as  new 
moon,  and  her  circuit  is  complete.  The  sun  has  been  apparently 
moving  toward  the  cast  among  the  stars  during  the  whole  month,  so 
that  during  the  interval  from  one  new  moou  to  the  next  the  moon 
has  to  make  a  complete  circuit  relatively  to  the  stars,  and  to  move 
forward  some  80'  further  to  overtake  the  sun,  which  has  also  been 
moving  toward  the  east  at  the  rate  of  1°  daily.  The  revolution  of 
the  moon  among  the  sUrs  is  performed  in  about  27^  days,*  so  that  if 
we  observe  when  the  moon  is  very  near  some  star,  we  shall  find  her 
in  the  same  position  relative  to  the  star  at  the  end  of  this  interval. 

Tlie  motion  of  the  moon  in  this  clrouit  differs  from  the  apparent 
motions  of  the  planete  in  being  always  forward.  We  have  seen  that 
the  planeU,  though,  on  the  whole,  moving  toward  the  east,  are 
effected  with  an  apparent  retrograde  motion  at  certain  intervals,  ow- 
ing to  the  motion  of  the  earth  around  the  sun.  But  the  earth  is  the 
real  centre  of  the  moon's  motion,  and  carries  the  moon  along  with  it 
in  its  annual  revolution  around  the  sun.  To  form  a  correct  idea  of 
the  real  motion  of  these  three  bodies,  we  must  imagine  the  earth  per- 
forming iu  cireuit  around  the  sun  in  one  year,  and  carrying  with  it 
the  moon,  which  makes  a  revolution  around  it  in  27  days,  at  a  dis- 
tance only  about  -^^  that  of  the  sun. 

PhaiM  of  the  Moon,— The  moon,  being  a  non-laminona 
body,  shines  only  by  reflecting  the  light  falling  on  her  from 
some  other  body.  The  principal  source  of  light  is  the  sun. 
Since  the  moon  is  spherical  in  shape,  the  sun  can  illumi- 
nate one  half  her  surface.  The  appearance  of  the  moon 
varies  according  to  the  amount  of  her  illuminated  hemi- 
sphere which  is  turned  toward  the  earth,  as  can  be  seen  by 
studying  Fig.  39.  Here  the  central  globe  is  the  earth; 
the  circle  around  it  represents  the  orbit  of  the  moon.  The  - 
rays  of  the  sun  fall  on  both  earth  and  moon  from  the 
right,  the  distance  of  the  sun  being,  on  the  scale  of  the 


*  More  enetlj,  r.mei*. 


^iMmmiiV:\!tic;r''m* 


B  she  i*  oppositlr 
Continuing  her 
un  on  the  other 
liya.  At  the  end 
merging  as  new 
been  apparently 
whole  month,  so 
>  next  tlie  moon 
rs,  and  to  move 
ch  has  also  been 
le  revolution  of 
days.*  so  that  if 
re  shall  find  her 
this  interval, 
tm  the  apparent 
i  have  seen  that 
i  the  east,  are 
a  intervals,  ow- 
the  earth  is  the 
an  along  with  it 
correct  idea  of 
le  the  earth  per* 
»rrying  with  it 
7  days,  at  a  dis- 


lon-lominoas 
I  on  her  from 
ht  is  the  ran. 
!  can  illami- 
>f  the  moon 
mated  hemi- 
m  be  seen  by 
is  the  earth; 
moon.  The 
on  from  the 
scale  of  the 


MOTIONS  AND  ATTRACTION  OF  THE  MOON.    126 

figure,  some  30  feet.  Eight  positions  of  the  moon  are 
shown  aronnd  the  orbit  at  A,  E,  C,  etc.,  and  the  nght- 
hand  hemisphere  of  the  moon  is  iUuminated  in  each  posi- 
tion. Outside  these  eight  positions  are  eight  others  show- 
ing how  the  moon  looks  as  seen  from  the  earth  in  each 

position. 
At  A  it  is  "new  moon,"  the  moon  being  nearly  between 


Vtob  Mi 


the  earth  and  the  ran.  Its  dark  hemisphere  is  then  trnn- 
ed  toward  the  earth,  so  that  it  is  entirely  invisible.  The 
sun  and  moon  then  rise  and  set  together. 

At  E  the  obserrer  on  the  earth  sees  about  a  fourth  of 
the  iUuminated  hemisphere,  which  looks  like  a  crescent,  a0 
shown  in  the  outside  figure.  In  this  position  a  great  deal 
of  light  is  refl«oted  from  the  earth  to  the  moon,  rendering 


126 


ASTnoNOitr. 


the  dark  part  of  the  latter  visible  by  a  gray  light.  Thi« 
appearance  is  Bometimes  called  the  "old  moon  in  the  new 
moon's  arms."  At  C  the  moon  is  said  to  be  in  her  "  first 
quarter,"  and  one  half  her  illuminated  hemisphere  is  visi- 
ble.  The  moon  is  on  the  meridian  at  6  p.m.  At  Q  three 
fourths  of  the  illuminated  hemisphere  is  visible,  and  at  B 
the  whole  of  it.  The  latter  position,  when  the  moon  is 
opposite  the  sun,  is  called  "full  moon."  The  moon  rises 
at  sunset  After  this,  at  H,  D,  F,  the  same  appearances 
are  repeated  in  the  reversed  order,  the  position  D  beinir 
called  the  "  lust  quarter." 


Thx  TiBtt 

H  is  not  possible  in  an  elementary  treaUse  to  give  a  comnlete  ae- 

.TaniVntl'T"'  ^^V"™  ""•"' '«^'"'  duei  tbe  S  oMhe 
Bun  and  moon.  A  general  account  may  be  presented  which  will  tw 
Wffldent  to  show  the  n.t«™  „f  tbe  iects'^rodu^  and  o7 Ih 

Let  us  consider  the  earth  to  be  composed  of  a  solid  centr*  sar 
rounded  by  an  ocean  of  uniform  (and  luTvery  grea  depth  S 
moon  exerciws  an  attraction  upon  every  particlJ  of  the  earth's  masi 
«.Hd  and  fluid  alike.  The  attraction  of  ule  whole  mooT(^)  ™^^ 
a  particle  m  is  — ^,  where  p  is  the  distance  frt.m  the  centre  of  the 
moon  to  m.    If  m  is  one  of  the  solid  particles  of  the  earth   It  cannot 

■olid  particles  move,  since  the  earth  proper  is  rigid 

If  m  is  a  fluid  particle,  it  is  free  to  move  in  obedience  to  the  forties 
impressed  upon  It.  Tlio  attraction  of  JTis  proportional  to  -*-;  that  is. 
the  particjes  nearest  Mm  most  attracted,  apd.on  the  whole  thi 
wajer^  the  part  of  the  earth  nearest  the'm'ook  iiil  be  .J^i  f 

The  moon  also  attracts  the  solid  parts  of  the  earth  moi«  th..  .i.- 

the  same  efect  as  if  there  was  another  moon  M  exactly  ODDodte  to 
Jf.  TlH»  elevation  of  the  water  under  Jf  ■  w  '  aoriw  aouE  m  .^ 
M  that  under  Jf.  on  account  of  the  incre«ed  disScTfSK  *^ 


'v«^!ft5' 


»y  light.  Thi8 
oon  in  the  new 
e  in  her  "  first 
lisphere  is  visi- 
f.  At  G  three 
liblo,  and  at  B 
1  the  moon  is 
'he  moon  rises 
le  appearances 
lition  D  being 


e  a  complete  ac- 
tbe  effect  of  tbc 
d  which  will  be 
ed  and  of  their 

«Hd  centre  sar- 
at)  depth.  The 
be  earth's  mass, 
moon  (M)  upon 

le  centre  of  the 

earth,  it  cannot 
«s  all  the  other 

ice  to  the  f  oitiea 
»lto-^-;thatis, 

the  whole,  the 
II  be  raised  to- 
more  than  she 
oduces  exactly 
tly  opposite  to 
!  qoite  as  gnat 
from  Jr. 


MOTIONS  AND  ATTRACTION  OF  THE  MOON.    127 

Thus  the  moon's  action  tends  to  elevate  the  whole  mass  of  water  on 
the  line  joining  her  centre  « ilh  the  cenl.-e  of  the  ca'"'.  ""fjl"*  »»  "J 
not  only  on  the  part  of  this  line  nearest  the  moon,  but  also  on  that 

'"l-hU  dev"i^'of  the  waters  of  the  ocean  above  their  mean  level  is 
called  the  tide.  The  tidal  effect  of  the  moon  produces  a  distortion  of 
Se  spherical  shell  of  water  which  we  have  supposed  to  f "^""d  Uie 
earth  and  elongates  this  shell  into  the  shape  of  an  ellipsoid,  the  longer 
Rxis  of  which  is  always  directed  to  the  moon.  Now  as  the  moon 
Tv^  a^und  the  earth  once  in  24^  54-.  this  ellipsoidal  shape  must 
S^move  with  her.  The  crest  of  the  wave  directly  under  M  would 
come  back  to  the  same  meridian  every  24-  54".  The  outer  crest  (under 
M')  would  come  W  27-  after  the  first,  so  there  would  be  two  A,gh 
UdLltany  one  meridian  every  (lunar)  day.  The  fla'.  (and  largest) 
S  tide  would  be  at  the  time  of  the  moon's  visible  transit  over  he 
mfrldiun  The  second  high  tide  would  be  12^  27-  later,  when  the 
moon  was  on  the  lower  meridian  of  the  place. 

The  high  tides  occur  when  there  Is  more  water  than  the  mean 
depth,  and  between  these  high  tides  we  should  »'«'«><»«; 'J«>f;/''0 
?n  eS.  lunar  day.  Similarly  there  wouUl  be  two  high  tides  dally  at 
eacrmerullan,  due  to  the  attractive  force  of  the  sun.  These  would 
have  a  rl^rlod  of  24  hours  and  could  not  always  agree  with  the  unar 
hirii  tides  When  the  solar  and  lun:ir  high  tides  coincided  (at  new 
aS  fu  I  moon),  then  we  should  have  the  highest  UigU  tides  and  the 
lowest  low  tUles.  (These  arc  the  Spring  tides,  so  called.)  When  the 
mZ  and  the  sun  were  90»  apart  (moon  at  first  and  third  quarter  . 
Ihrwe  should  have  the  lowest  high  tides  and  the  highest  low  tlde^ 

^Z  iSprXclfg  U  of  the  moon  is  to  that  of  the  sun  a.  800  U 
to  855     The  great  mass  of  the  sun  compensates  in  some  degree  for 

oppose  each  other.    The  relaUve  heights  are  as  800 +885  :  800  -  855. 
or  as  la  to  5  approximately. 

The  explanation  above  relates  to  an  earth  covered  by  an  ocwn  ot 
uniform  depth.  To  fit  it  to  the  facU  as  they  are.  a  thousand  c Ir- 
cuSces  must  be  taken  into  aocount.  which  depend  upon  the 
mSlng  effects  of  continents  and  islands,  of  deer  and  Bhallow 
^  of  currente  and  winds.  Practically,  the  high  tide  at  any  sU- 
tion  I.  predicted  by  adding  to  the  time  of  the  moon's  transit  over 
its  merldUna  quantity  determined  from  obeorvatioB  w4  not  from 
ibeoty 


128 


ABTHONOMr. 


:! 


IffMU  «f  tiM  XMm  .pM  tk«  Itftk'i  l«UMo«.-Ai  the  tide-waTe 
moves  It  meeu.  with  resisiauce  due  to  friciion.  The  amount  of  thia 
rasistance  u  subtracted  daily  from  the  earth's  energy  of  roution 
The  tides  act  on  the  earth,  in  a  way.  as  if  they  wen  a  light  friction'- 
brake  applied  to  an  enormously  heavy  wheel  turning  rapidly  The 
wheel  has  been  set  to  turning,  and,  so  far  as  we  know,  it  will  never 
have  any  more  rotative  energy  given  to  it.  Every  subtracUon  of 
energy,  however  small,  k  a  positive  and  irretrievable  loss. 

The  lunar  tides  are  gradually,  though  very  slowly,  lengthening  the 
day  Since  accurate  astronomical  observations  began  there  has  been 
no  dmrvaHonal  proof  of  any  apprectable  change  in  the  length  of  the 
day.  but  the  change  has  been  going  on  nevertheless. 


_i 


As  the  tide-WATe 
le  amount  of  this 
ergy  of  roUtion. 
«  a  light  friction- 
ig  rapidly.  The 
low,  it  will  nerer 
7  subtraction  of 
eloas. 

.  lengthening  the 
in  there  has  been 
the  length  of  the 


CHAPTER  VIII. 

ECLIPSES  OP  THE  SUN  AND  MOON. 

Eclipses  are  phenomena  nriBing  from  the  shadow  of  one 
hody  being  cast  upon  another,  or  from  a  dark  body  paaaing 
oyer  a  bright  one.  In  an  eclipse  of  the  sun,  the  shadow  of 
the  moon  sweeps  over  the  earth,  and  the  sun  is  wholly  or 
partially  obscured  to  observers  on  that  part  of  the  earth 
where  the  shadow  falls.  In  an  eclipse  of  the  moon,  the 
latter  enters  the  shadow  of  the  earth,  and  is  wholly  or 
partially  obscured  in  consequence  of  being  deprived  of 
some  or  all  of  its  borrowed  light.  The  satellites  of  other 
planets  are  from  time  to  time  eclipsed  in  the  same  way  by 
entering  the  shadows  of  their  primaries ;  among  these  the 
satellites  of  Jupiter  are  objects  whose  eclipses  may  be 
observed  with  great  regularity. 

THI  EAETH*!  taASOW  AHD  FBVmiBXA. 

In  Fig.  40  let  8  represent  the  sun,  and  E  the  earth.  Draw  straight 
lines,  DBF  and  J^BV,  each  Ungent  to  the  sun  and  the  earth. 
The  two  bodies  being  supposed  spherical,  tliese  lines  will  be  the 
inteisections  of  a  cone  with  the  plane  of  the  paper,  and  may  be 
taken  to  represent  that  cone.  It  is  evident  that  the  cone  B  YB  will 
be  the  outline  of  the  shadow  of  the  earth,  and  that  irrithin  this  cone 
no  direct  sunlight  can  penetrate.  It  is  therefore  called  the  earth's 
«AadlMe-«MW. 

Let  us  also  draw  the  lines  BBP  and  PBP'  to  represent  the 
other  cone  tangent  to  the  sun  and  earth.  It  is  then  evident  that 
within  the  region  VBP  and  VBP'  the  light  of  the  sun  wiU  b« 
partially  but  not  entirely  cut  off, 


130 


ASTRONOMT. 


Dimeniiona  of  Shadow.— Let  ui  investigate  the  distance  E  V  from 
the  centra  of  tbc  eartli  to  tbe  vertex  of  tlie  sliudow.  Tlie  triangles 
VEB  and  V8D  are  siiniiar,  Imving  a  riglit  angle  at  B  and  at  D. 
Hence 

VE:ED=  VS :  8  D  =  ES :  {HD-  EBf. 

So  if  we  put 

I  =  VE,  tlie  lengtli  of  tlio  shadow  measured  from  the  centre  of 
tlio  earth. 
r=  E8,  the  radius-vector  of  the  earth, 
B=  8D,  the  radius  of  the  sun, 
p  =  EB,  the  radius  of  the  earth, 


we  have 


l=VE  = 


E8X  EB 
81) -EB 


Tm.  40.— row  o»  ■uaov. 

That  is,  I  k  expresaed  in  terms  of  known  quontltiM^  imi  thtw  la 
known. 

The  radius  of  the  shadow  dimlnisliea  uniftmnly  with  the  diatanco 
«s  wo  go  outward  from  the  «arth.    At  any  distanoo  s  from  tlie 

earth's  centre  it  will  be  ei^ua)  to  II  —'^P,  for  this  formula  fives 

the  radius  p  when  s  s=  <^  and  the  diameter  aero  wkcn  f  =  <  as  it 
should.* 


•  It  wlllbe  noted  that  this  ezprtMkm  is  not,  i1goraitol7  sfMU^b  the  I 
dlooMter  of  the  ihadow,  Iwt  (he  ahorteat  dlitiince  fram  a  potoit  on  (ta  osatral 
IliM  to  its  conioai  pnifsoo.  Tliis  dtatance  is  ineaaared  ia  a  tfirsdioB  XB  parpen- 
dienlartoDB.wheraiMtlM  diameter  would  lie  perpendleular  totho  aidS^A 
anditahaU-laaclhwoMldJMalttUei  *      — 


listance  E  V  from 
ow.  The  triangles 
igle  at  B  and  at  D. 

-KBj. 


from  tke  centre  of 


J 


itltiMb  Md  tims  H 

with  |he  distance 
itanoo  t  from  tlie 

his  formula  fires 

>  when  I  =  I  as  it 


rSfMttW.tlMI 

apotatoa  (taoMtral 
dJTMtkmXBpeipen- 
Mlartotteaitti^i;, 


ECLIPSES  OF  THE  SUN  AND  MOON. 


loufm  cr  THi  Xooi. 


181 


The  mean  distance  of  the  moon  from  the  earth  is  abotit 
60  radii  of  the  latter,  and  the  length  E  Vot  the  earth's 
shadow  is  217  radii  of  the  earth.  Hence  when  the  moon 
passes  through  the  shadow  she  does  so  at  a  point  less  than 
three  tenths  of  the  waj  from  Eio  V.  The  radios  of  the 
shadow  here  will  be  'Vrf^  <>'  ^^^  radius  E  B  ot  the  earth, 
a  quantity  which  we  readily  find  to  be  about  4600  kilo- 
metres. The  radios  of  the  moon  being  1736  kilometres,  it 
will  be  entirely  enveloped  by  the  shaduw  when  it  passes 
through  it  within  2864  kilometres  of  the  axis  EVot  the 
shadow.  If  its  least  distance  from  the  axis  exceed  this 
amount,  a  portion  of  the  lunar  globe  will  be  outside  the 
limits  BV  ot  the  shadow-cone,  and  will  therefore  receive  a 
portion  of  the  direct  light  of  the  sun.  If  the  least  distance 
of  the  centre  of  the  moon  from  the  axis  of  the  shadow  is 
greater  than  the  ram  of  the  radii  of  the  moon  and  the 
shadow — that  is,  greater  than  6336  kilometres — the  moon 
will  not  enter  the  shadow  at  all,  and  there  will  be  no  eclipse 
proper,  thongh  the  brilliancy  of  the  moon  is  diminished 
wherever  she  is  within  the  pennmbral  region. 

Wlien  an  eclipse  of  the  moon  occurs,  the  phases  are  laid  down 
in  tlw  almanac.  (See  Fig.  40.)  Botipaiing  the  moon  to  he  moving 
arouad  the  earth  from  helow  upwiud,  its  advancing  edge  first 
meets  the  Iwundaiy  BP'  of  the  penumbra.  The  time  of  this 
ooouireaoe  is  given  in  the  almanac  as  that  of  "  moon  entering 
penatthra."  A  small  portion  of  the  suslight  is  then  cut  off  from  the 
advaodng  edge  of  the  moon,  and  this  amount  constantly  increases 
until  the  edfe  icadies  the  houndary  ^  F  of  the  shadow.  It  is 
cuffons,  however,  that  the  eye  can  scarcely  delect  any  diminution  in 
tlife  liriiliaaey  of  the  moon  until  she  has  almost  toudied  Uie  boundary 
of  tlte  «hado«<  The  observer  must  not,  therefore,  expect  to  detect  the 
OOfniuf  eclipse  witn  vary  nearly  Uif  lips  |ivei|  ip  t)ie  stpaoae  as  that 


183 


ASTRONOMY. 


of  "moon  entering  ■hadow."  At  this  happens,  the  advancing 
portion  of  tlie  lunar  disk  will  be  entirely  lost  to  view,  as  if  it  were 
cut  off  by  a  rather  lll-deflned  Hoe.  It  takes  the  moon  about  an  hour 
to  m6ve  over  a  distance  equal  to  her  own  diameter,  so  that  if  the 
eclipse  is  nearly  central  the  whole  moon  will  be  immersed  in  the 
shadow  about  an  hour  after  she  flrst  strikes  it.  This  is  the  time  of 
beginning  of  total  eclipse.  80  long  as  only  a  moderate  portion  of 
the  moon's  disk  is  in  the  shadow,  that  portion  will  be  entirely 
invisible,  but  if  the  eclipse  becomes  total  the  whole  disk  of  the  moon 
will  nearly  always  be  plainly  visible,  shining  with  a  red  coppery 
light.  This  is  owing  to  the  refraction  of  the  sun's  rays  by  the  lower 
straU  of  the  earth's  atmosphere.  We  shall  see  hereafter  that  If  a  ray 
of  light  D  B  passes  from  the  sun  to  the  earth,  so  as  Just  to  grau  th« 
latter,  it  is  bent  by  refraction  more  than  a  degree  out  of  its  course, 
so  that  at  th>i  distance  of  the  moon  the  whole  shadow  of  the  earth 
Ui  filled  with  t;<is  refracted  light.  An  observer  on  the  moon  would, 
during  a  total  eclipse  of  the  latter,  see  the  earth  surrounded  by  s 
ring  of  light,  and  this  ring  would  appear  red,  owing  to  the  absorp- 
tion of  tiie  blue  and  green  rays  by  the  earth's  atmospliere.  Just  as  the 
sun  seems  red  when  setting. 

The  moon  may  remain  enveloped  in  the  shadow  of  the  earth 
during  a  period  ranging  from  a  few  minutes  to  nearly  two  hours, 
according  to  the  distance  at  which  she  posses  from  the  axis  of  the 
shadow  and  the  velocity  of  her  angular  motion.  When  she  leaves 
the  shadow,  the  phases  which  we  have  described  occur  in  reverse 
order. 

It  very  often  happens  that  tiie  moon  passes  through  the  penumbra 
of  the  earth  without  touching  the  shadow  at  all.  The  diminution  of 
light  in  sueh  cases  is  scarcely  perceptible  unless  the  moon  at  least 
grazes  the  edge  of  the  shadow. 


Xounti  Of  TBI  8w. 

In  Fig.  40  we  may  rappow  B  E  B*  io  repreaent  the 
moon.  The  geometrical  theory  of  the  shadow  will  remun 
the  same,  though  the  actual  length  of  the  shadow  in 
miles  will  be  much  less.  The  mean  length  of  the  moon's 
shadow  cast  by  the  sun  is  377,000  kilometres.  This  is 
nearly  equal  to  the  distance  of  the  moon  from  the  earth 
when  ibe  n  in  oonjanctioti  with  the  waA.   We  ttiere(OT<i 


w 


ECUP8B8  OF  THE  SUN  AND  MOON. 


133 


I,  the  advancing 
lew,  as  if  it  were 
on  about  an  hour 
ler,  so  that  if  the 
immeraed  in  tho 
Ilia  is  the  time  of 
derate  portion  of 

irlll  be  entirely 
disk  of  the  moun 
th  a  red  coppery 
rays  by  the  lower 
•f  ter  that  If  a  my 
I  Just  to  grau  th« 
out  of  its  course, 
tdow  of  the  earth 
the  moon  wonld, 

surrounded  by  a 
log  to  the  absorp- 
tpliere,  Just  as  the 

low  of  the  earth 
nearly  two  hours, 
m  the  axis  of  the 
When  atae  teavea 
occur  in  reverse 

igh  the  penumbr* 
rhe  diminution  of 
the  moon  at  leaat 


>  repreaent  the 
low  will  remun 
the  shadow  in 
li  of  the  moon's 
letres.  This  is 
from  the  Murth 
Wo  tnOfofOTO 


conclude  thst  when  the  moon  passes  between  the  earth 
and  the  sun,  the  former  will  be  very  near  the  vertex  V  of 
the  shadow.  As  a  matter  of  fact,  an  observer  on  the 
eurth'a  surface  will  sometimes  pass  through  the  region 
C  VC,  and  sometimes  on  tho  other  side  of  V. 

Now,  in  Fig.  40,  still  supposing  BBS  to  be  the  moon,  and 
<8Di)'  to  be  the  sun,  let  us  draw  the  lines  DBf  and  DBP  tan. 
gent  to  both  moon  and  sun,  but  crossing  each  other  between  these 
bodies  at  b.  It  is  evident  that  an  observer  outside  the  space 
PBBP  will  see  the  whole  sun,  no  part  of  the  moon  being  project- 
ed upon  it;  while  within  this  space  the  sun  will  be  more  or  less 
obscured.  The  whole  obsoured  space  may  be  divided  into  three 
regions,  in  eaeh  of  which  the  character  of  the  phenomenon  is  dif- 
ferent. 

First,  we  have  the  region  BVB  forming  the  shadow-cone  proper. 
Here  the  sunlight  is  entirely  cut  off  by  the  moon,  and  darkness  is 
therefore  complete,  except  so  far  as  light  may  enter  by  refraction 
or  reflection.  To  an  observer  .at  V  the  moon  would  exactly  cover 
the  sun.  the  two  bodies  being  apparently  tangent  to  cnch  other  all 
around. 

Secondly,  we  have  the  conical  region  to  the  right  of  F  between 
the  lines  B  V  and  B  Fcontinucd.  In  this  region  the  moon  is  seen 
wholly  projected  upon  the  sun.  the  visible  portion  of  the  latter 
presen.'  ng  the  form  of  a  ring  of  light  around  tlie  moon.  This  ring 
of  light  will  be  wider  in  proportion  to  the  apparent  diameter  .of  the 
sun,  the  farther  out  we  go,  because  the  moon  will  appear  smaller 
than  the  sun,  and  its  angular  diameter  will  diminish  in  a  more' rapid 
ratio  than  that  of  the  sun.  This  regton  is  that  of  annvlar  tdip»e, 
because  the  sun  will  present  the  appearance  of  an  annulus  or  ring  of 
light  around  the  moon. 

Thirdly,  we  have  the  region  PB  V  and  FB  V,  which  we  notice 
is  eontinuoas,  extending  around  the  interior  cone.  An  observer 
here  would  see  the  moon  partly  projected  upon  the  sun,  snd  there, 
fore  a  certain  part  of  the  sun's  light  would  be  cut  off.  Along  the 
inner  boundary  B  Y  and  B  V  tlie  obscuration  of  the  sun  will  be 
complete,  but  the  amount  of  sunliglit  will  gradually  increase  out  to 
the  outer  boundary  BPB  P,  where  the  whole  sun  is  visible,  This 
region  of  partial  otiaeuration  is  called  the  jwniraitria. 

To  aiww  more  eleariy  the  phenomena  of  sofaur  eeHpsM,  iri  present 
Miotber  figure  reprvssnting  the  penambnt  Of  the  mooo  thrown  upon 


'm 


1" 


184 


ASTRONOMY. 


the  cftrth.*  The  o»t«r  of  (he  two  circlee  8  lepreMnU  the  limb  of  Um 
■un.  The  exterior  Inngcntt  which  niKrk  the  boundary  of  the  ihadov 
eroM  each  other  nt  Y  before  reaching  the  earth.  The  earth  (K)  being 
a  little  beyond  the  verlei  of  the  iluulow,  there  can  be  no  total  eclipae. 
In  thia  oHe  an  obaerver  In  the  penumbral  region,  VO  or  DO,  will 
aee  the  moon  p*rtly  projected  on  the  nin,  while  If  he  chance  to  bo 
altuatcd  at  O  he  wll'i  we  au  annular  eclipae.  To  iiliow  how  this 
is,  wa  draw  dotted  iiaes  from  0  tangent  to  the  moon.  The  angle 
iMtween  these  lines  ripraaents  the  apparent  diameter  of  the  moon  as 
seen  from  the  eartli.  Continuing  them  to  the  sun,  tliey  show  the 
apparent  dkmeter  of  the  moon  as  projected  upon  the  sun.  It  will 
bo  seen  that,  In  \\%a  case  supposed,  when  the  rertex  of  the  shadow 
'is  between  tlia  earth  and  moon  the  Utter  will  necessarily  appear 


rra.  41.— rievu  or  Sbabov  mb  Amirilab  Boumb. 


smaller  than  the  sun,  and  the  observer  will  aee  a  portion  of  the  solar 
disk  on  all  sides  of  the  moon,  as  shown  in  Fig.  48. 

If  the  moon  were  a  little  nearer  the  earth  than  it  is  represented 
in  Fig.  41,  it*  shadow  would  reach  the  earth  in  the  neighborhood 
of  0.  We  should  then  have  a  total  eclipse  at  each  point  of  the  earth 
on  which  it  fell.  It  wilt  be  seen,  however,  that  a  total  or  annuhur 
•clipse  of  the  sun  is  visible  only  on  a  very  small  portion  of  the  earth's 
surface,  because  the  distance  of  the  moon  clianges  ao  little  that  tlie 
Mfth  can  nevnr  be  far  from  the  vertex  V  of  the  shadow.    As  the 

•n  will  be  acted  that  all  the  icurN  of  aelipsM  ai*  Mosspaiiljr  drawn  ve. 
mwheoioCproiwrtloib  BMllyth*  sua  is400tiaMO  thedlsttiii^of.themooii, 
wMsfc  agaia  Is  eottaMstharadiasaC  the  earth.  But  It  wa^lil  |ie  entlrelj  ion- 
passtMe  to  draw  a  flfure  o<  this  propertlon;  we  are  theretors  obliged  to 
iiHBHHlth»  sarth  la  fig.  4Baalaftertttsat(MpiB,itnd  the  moon  «i«mrlir 
halt  wer  Ntwsaa  tt)9  earth  and  sua. 


M  limb  of  Um 
>f  the  •hador' 
trlh(/?)  being 
I  total  fclipM. 

0  or  DO,  will 
chance  to  be 

low  bow  Ibis 
I.  The  angle 
f  the  moon  ■■ 
ibey  ibow  I  be 
•un.    It  will 

1  Ibo  iliadow 
laarily  appear 


<a  of  the  aolar 

la  represented 
neigbborbood 
It  of  the  earth 
a\  or  annuhur 
of  the  earth's 
little  that  the 
dow.    As  the 

llKjr  drawn  v». , 
ffo(. the  moon, 
I  Itemtiraljim- 
tors  obUgeil  to 

www  fl^^^jfSf 


XOLIPSRS  OF  rOB  StTN  AltD  MOOif. 


18ft 


on  Bra  Boaoie  am  AnraLAB  Bourca. 


Inoon  moves  around  the  earth  from  west  to  east,  its  shadow,  whether 
the  eclipse  be  total  or  annuUr,  moves  In  the  same  direction.    The 

diameter  of  the  shadow  at  the  

surf  nee  of  the  earth  ranges  from 
cero  to  100  miles.  It  therefore 
sweeps  along  a  belt  of  the 
earth's  surface  of  that  breadth, 
In  the  same  direction  in  whioli 
the  earth  Is  rotating.  The 
Telocity  of  the  moon  relative  to 
the  earth  being  8400  kilometraa 
per  hour,  the  shadow  would 
pass  along  with  this  velocity  If 
the  earth  did  not  rotate,  but 
owing  to  the  eartli's  rotation 
the  velocity  relative  to  points 
on  Its  surface  may  range  from 
9000  to  8400  kilometres  (1800 
to  SlOO  miles). 

The  reader  will  readily  understand  that  in  order  to  see  a  total 
eclipse  an  observer  must  station  himself  beforehand  at  some  point  of 
the  earth's  surface  over  which  the  shadow  Is  to  pass.  Tliese  points 
are  generally  calouUted  some  years  in  advance,  in  the  aatronomical 
ephemerldea. 

It  will  be  aeen  that  •  partial  eclipse  of  the  ran  may  be 
Tisible  from  a  mach  larger  portion  of  the  earth's  rarface 
than  a  total  or  annular  one.  The  apace  CD  (Fig.  41)  orer 
which  the  penambra  extendi  ia  generally  of  about  one  half 
the  diameter  of  the  earth.  Rooghly  speaking,  a  partial 
eclipae  of  the  ran  may  aweep  over  a  portion  of  the  earth'a 
aurface  ranging  from  lero  to  perhaps  one  fifth  or  one  aizth 
of  the  whole. 

There  are  really  more  eclipaea  of  the  raa  than  of  the 
moon.  A  year  never  paaaea  without  at  leaat  two  of  the 
former,  and  aometimea  five  or  aiz,  while  there  are  rarely 
more  than  two  eclipaea  of  the  moon,  and  in  many  yeara 
none  at  all.    Bat  at  any  one  place  more  eclipaea  of  the 


•mmmmmssm^ 


186 


A8TR0N0MT. 


moon  will  be  seen  than  of  the  san.  The  reason  of  this  is 
that  an  eclipse  of  the  moon  is  yisible  over  the  entire  hemi< 
sphere  of  the  earth  on  which  the  moon  is  shining,  and  as 
it  lasts  several  honrs,  observers  who  are  not  in  this  hemi- 
sphere  at  the  beginning  of  the  eclipse  may,  by  the  earth's 
rotation,  be  brought  into  it  before  it  ends.  Thus  the 
eclipse  will  be  seen  over  more  than  half  the  earth's  surface. 
But,  as  we  have  just  seen,  each  eclipse  of  the  sun  can  be 
seen  over  only  so  small  a  fraction  of  the  earth's  surface  as 
to  more  than  compensate  for  the  greater  absolute  fre- 
qnency  of  solar  eclipses. 


Fio.  4S.— OoMPAMaoH  or  Smadow  amo  PBiiuin»A  or  lUKm  im  Momr.   A  a 

THE  POUnOM  OP  TBI  If  OOM  DOMWO  A  SobAB,  B  DUBIH*  A  LVRAa,  ■OLIPM. 

It  will  be  seen  that,  in  order  to  have  either  a  total  or 
•nnnlar  eclipse  visible  npon  the  ewrth,  the  line  joining 
the  O0ntres  of  the  sun  and  moon,  being  continued,  must 
strike  the  earth.  To  an  observer  on  this  line  the  centres 
of  the  two  bodies  will  seem  to  coincide.  An  eclipse  in 
which  this  occurs  is  called  a  central  one,  whether  it  be 
total  or  annular.  Fig.  43  will  perhaps  aid  in  giving  a 
clear  idea  of  the  phenomena  of  eclipses  of  both  sun  and 
moon. 


i  I 


iHX  uovmmei  or  xoums. 

If  tbe  orbit  of  the  moon  around  the  earth  were  in  or  near  the 
plane  of  tbe  ecliptic  there  would  be  an  eclipse  of  tbe  sun  at  every 
Mw  moon,  and  an  eelipae  of  tbe  moon  at  every  full  moon.    But, 


ion  of  this  ia 
I  entire  hemi- 
ining,  and  as 
in  this  bemi- 
\}y  the  earth's 
3.  Thus  the 
irth's  surface, 
e  sun  can  be 
li's  surface  as 
absolute  fre- 


I  im  Hook.  A  u 
%KoLinc. 

ler  a  total  or 
I  line  joining 
itinned,  must 
e  the  centres 
An  eclipse  in 
rhether  it  be 
I  in  giving  a 
xtth  sun  and 


in  or  near  the 
le  sun  at  every 
ill  moon.    Bat, 


i 


SOLIPSBS  OF  TBS  BUK  AND  MOON. 


137 


owing  to  the  inclination  of  the  moon's  orbit,  the  shadow  and  penum- 
bra of  the  moon  commonly  pass  above  or  below  the  earth  at  the  time 
of  new  moon,  while  the  moon,  at  her  full,  commonly  passes  above 
or  below  tbe  shadow  of  the  earth.  It  is  only  when  the  moon  is 
near  its  node  at  the  moment  of  new  or  full  moon  that  an  eclipse  can 
occur. 

Tbe  question  now  arises,  how  near  must  tlie  moon  be  to  its  node 
in  order  that  an  eclipse  may  occur  T  It  is  found  that  if,  at  tbe 
moment  of  new  moon,  tlie  moon  is  more  than  18° -B  from  its  node 
no  eclipse  of  tbe  sun  is  possible,  while  if  it  is  less  than  18° '7  an 
eclipse  is  certain.  Between  tlieae  limits  an  eclipse  may  occur  or  fail 
according  to  the  respective  distances  of  the  sun  and  moon  from  the 
earth.    Half  way  between  these  limits,  or  say  16°  from  the  node,  it 


FM  44.— maitratiiwtaMrMliiiMatdMremtdiBlaaetafromtiMiiode.  Hm 
*H*  *<Uw  •!•  the  .arth's  l**>ow.  the  cwitre  of  which  Is  always  to  the  ediptic 
ZS.  mTmooii*.  orbit  to  repn^nted  by  CD.  At  O  U-  eelipw  to  eMtial  and 
tom.  at  J"  It  to  iiartial,  and  at  X  there  to  bwreiy  an  eeUpee. 

is  an  even  chance  timt  an  edlpae  will  occur;  toward  the  lower  limit 
(18* -7)  the  ebances  increase  to  certainty;  toward  the  upper  one 
(W.*)  they  diminish  to  aero.  The  corresponding  limits  for  an 
eclipse  of  tbe  moon  are  V  and  18*' ;  that  is.  If  at  the  moment  of  full 
moon  the  distance  of  the  moon  from  her  node  is  greater  than  12i° 
no  eclipee  can  occur,  while  If  the  distance  is  less  than  8°  an  eclipse 
Is  certain.  We  may  pat  the  mean  limit  at  11*.  Since.  In  the  long- 
run,  new  aud  fuH  moon  will  occur  equally  at  all  disUnces  from  the 
node,  there  will  be,  on  the  average,  aiiteen  edipaes  of  the  sun  to 
eleven  of  the  moon,  or  nearly  fifty  per  cent  more. 

If,  at  the  moment  of  new  moon,  the  distance  of  the  moon  from 
the  node  is  leas  than  lOi*  there  will  be  a  central  eclipse  of  the  sua, 
and  If  greater  than  tiiia  there  will  not  be  such  an  eclipse.    The 


K-i 


138 


ASTBONOMT. 


eclipse  limit  may  range  half  a  degree  or  more  on  each  side  of  this 
mean  value,  owing  to  the  varying  distance  of  the  moon  from  the 
earth.  Inside  of  10°  a  central  eclipse  may  be  regarded  as  certain, 
and  outside  of  11°  as  impossible. 

If  the  direction  of  the  moon's  nodes  from  the  centre  of  the  earth 
were  invariable,  eclipses  could  occur  only  at  the  two  opposite  months 
of  the  year  when  the  sun  had  nearly  the  same  longitude  as  one  node. 
For  instance,  if  the  longitudes  of  the  two  opposite  nodes  were  re- 
spectively 64°  and  284°,  then,  since  the  sun  must  be  within  18°  of 
the  node  to  allow  of  an  eclipse  of  the  moon,  its  longitude  would  have 
to  be  either  between  43°  and  66*,  w  between  822°  and  246".  But 
the  sun  is  within  the  first  of  these  regions  only  in  the  month  of  May, 
and  within  the  second  only  during  the  mouth  of  November.  Hence 
lunar  eclipses  could  then  occur  only  during  the  months  of  May  and 
November,  and  the  same  would  hold  true  of  central  eclipses  of  the 
sun.  Small  partial  eclipses  of  the  latter  might  be  seen  occasionally 
a  day  or  two  from  the  beginnings  or  ends  of  the  above  months,  but 
they  would  be  very  small  and  quite  rare.  Now,  the  nodes  of  the 
moon's  orbit  were  actually  in  thft  above  directions  in  the  year  1878. 
Hence  during  that  year  eclipses  occurred  only  in  May  and  No- 
vember. We  may  call  these  months  the  seasons  of  eoUpaes  for 
1878. 

There  is  a  retrograde  motion  of  the  nooh's  nodes  amouhting  to 
IQi"  in  a  year.  The  nodes  thus  move  back  to  meet  the  sua'  in  ita 
annual  revolution,  and  this  meeting  occurs  about  80  days  earlier 
every  year  than  it  did  the  year  before.  The  result  is  that  the  season 
of  eclipses  is  constantly  shifting,  so  that  each  season  ranges  through- 
out the  whole  year  in  18-6  years.  For  instance,  the  season  corre- 
sponding to  that  of  November,  1878.  had  moved  back  to  July  and 
August  in  1878,  and  will  occur  in  May,  1882,  while  that  of  May, 
1878,  will  be  shifting  back  to  November  in  1888. 

It  nuy  be  interesting  to  illustrate  this  by  giving  the  days  in  which 
the  sun  is  in  conjunction  with  the  nodes  of  the  moon's  orbit  during 
several  years. 


Awtadinfllode. 


1879. 
1880. 
1880. 
1881. 


If! 


1888. 
1884. 


January  SM. 
January  6. 
December  18. 
November  80. 
November  18. 
October  25. 
Octobers. 


Descendiiir  iTo^. 

1879.  July  17. 
June  27. 
June  8. 
May  80. 
Mayi. 

1884.  April  IS. 

1885.  MaivbSS. 


1880. 

lasi. 

1888. 


sach  side  of  this 

moon  from  tbe 

irded  as  certain, 

itre  of  th«  wrtli 
opposite  months 
ude  as  one  node. 
)  uodes  were  re- 
be  within  12°  of 
Itude  would  hare 
and  246°.  But 
e  month  of  Majr, 
•▼ember.  Henoe 
mtha  of  May  and 
I  eclipses  of  the 
een  occasionally 
ove  months,  but 
lie  nodes  of  the 
a  th*  year  1878. 
I  Uttf  fend  No- 
ot  eoUpJMS  for 

«  amouhting  to 
t  the  sua  in  its 

M  days  earlier 
I  that  the  season 

ranges  through- 
lie  season  oorre- 
•ck  to  July  and 
le  that  of  May, 

le  days  in  which 
n's  orbit  during 


Node. 

yl7. 

ieS7. 

leS. 

yao. 

rillS. 
rah  as. 


EOLIPSSS  OF  THE  SUN  AND  MOON. 


1S9 


During  these  years,  eclipees  of  the  moon  can  occur  only  within  11 
or  12  days  of  these  dates,  and  eclipses  of  the  sun  only  within  IS  or 
16  days. 

In  consequence  of  the  motion  of  the  moon's  node,  three  Taiying 
angles  come  into  play  in  considering  the  occurrence  of  an  eclipse: 
tbe  longitude  of  the  node,  that  of  the  sun,  and  that  of  the  moon. 
One  revolution  of  the  moon  relatirely  to  the  node  is  accomplished, 
on  tbe  average,  in  27  21222  days.  If  we  calculate  tbe  time  required 
for  the  sun  to  return  to  the  node,  we  shall  find  it  to  be  846-6201 
days. 

Now,  let  us  suppose  the  sun  and  moon  to  start  out  together  from 
a  node.  At  the  end  of  846>6201  days  tbe  sun,  baring  apparently 
performed  nearly  an  entire  revolution  around  the  celcsthil  sphere,  will 
again  be  at  tbe  same  node,  which  has  moved  back  to  meet  it.  But  the 
moon  will  not  be  there.  It  will,  during  the  interval,  have  passed 
the  node  12  times,  and  the  18th  passage  will  not  occur  for  a  week. 
The  same  thing  will  be  true  for  18  successive  returns  of  the  sun  to 
the  node;  we  shall  not  find  tbe  moon  there  at  the  same  time  with 
the  sun;  she  will  always  have  passed  a  little  sooner  or  a  little  fatter. 
But  at  the  19th  return  of  the  sun  and  the  242d  of  the  moon,  the  two 
bodies  will  be  in  conjunction  witUn  half  a  degree  of  the  node.  We 
find  from  tlie  preceding  periods  that 

'  iv  turns  of  the  moon  to  the  node  require  688S.887  days. 


sun 


6SeS.780 


The  two  bodies  will  therefore  pass  the  node  within  10  hoars  of 
each  other.  This  conjunction  of  the  sun  and  moon  will  be  the  Mid 
new  moon  after  that  from  which  we  started.  Now,  one  lunatton 
(that  is,  the  interval  between  two  consecutive  new  mooas)  is,  in  the 
mean,  28.S80S88  days;  228  lunations  therefore  require  6688.12  days. 
The  new  moon,  therefore,  occurs  a  little  before  the  bodies  reach  the 
node,  the  distance  from  the  latter  being  that  over  whidi  the  moon 
moves  in  0*.086.  mr  the  sun  in  0'.490.  This  distance  is  28'  of  are, 
somewhat  less  than  the  apparent  semldiameter  of  either  body.  This 
would  be  the  smallest  distaaoe  from  either  node  at  which  any  aeW 
moon  would  occur  during  the  whole  period.  The  next  nearest  m>> 
proaches  would  have  occurred  at  the  8Sth  and  47th  lunations  re^ieo- 
tively.  The  8Sth  new  moon  would  have  occurred  about  6*  befoM 
the  two  bodies  arrived  at  the  node  from  Which  We  started,  aUd  tha 
47th  about  li*  put  the  opposite  node.  No  other  new  moon  wooM 
«enir  so  near  •  node  before  the  228d  one,  wMeh.  iswe  hare  jui* 
.^ML  weald  ooeurO*ar  wast  of  tbe  Boda.    ThIspethMlaf  MtatW 


tmmmnsmtii.-^,. 


140 


ABTRONOMY. 


moons,  or  18  yean  11  days,  was  called  the  Saro*  by  the  ancient  as- 
tronomers, and  by  means  of  it  tliey  predicted  ecli|>8e8. 

Tlie  possibility  of  a  total  eclipse  of  the  sun  arises  from  the  occa- 
sional very  slight  excess  of  the  apparent  angular  diameter  of  the 
moon  over  that  of  the  sun.  This  excess  is  so  slight  that  such  an 
eclipse  can  never  last  more  than  a  few  minutes.  It  may  be  of  inter- 
est to  point  out  tlie  circumstances  whicli  favor  a  long  duration  of 
totality.    These  are: 

(1)  That  the  moon  should  be  as  near  as  possible  to  the  earth,  or, 
technically  speaking,  in  perigee,  because  its  angular  diameter  as 
seen  from  the  earth  will  then  be  greatest. 

(2)  That  the  sun  should  be  near  its  greatest  distance  from  the 
earth,  or  in  apogee,  because  then  its  angular  diameter  will  lie  the 
least.  It  is  now  in  this  position  about  the  end  of  June;  hence  the 
most  favorable  time  for  a  total  eclipse  of  very  long  duration  is  in  the 
summer  moiiths.  Since  the  moon  must  be  in  perigee  and  also  be- 
tween the  earth  and  sun,  it  follows  tliat  the  longitude  of  the  perigee 
must  l)e  nearly  tliat  of  the  sun.  The  longitude  of  the  sun  at  the 
end  of  June  being  100°,  this  is  the  most  favorable  longitude  of  the 
moon's  perigee. 

(8)  Tiie  moon  must  be  very  near  the  node  in  order  tliat  the  centre 
of  the  shadow  may  fall  near  the  equator.  The  reason  of  this  condi- 
tion is  that  the  duration  of  a  total  eclipse  may  be  considerably  in- 
creased by  the  rotation  of  the  earth  on  its  axis.  We  have  seen  that 
the  shadow  sweeps  over  the  earth  from  west  toward  east  with  a 
Telocity  of  about  8400  kilometres  per  hour.  Since  the  earth  rotates 
in  the  same  direction,  the  velocity  relative  to  the  observer  on  the 
earth's  surface  will  be  diminished  by  a  quantity  depending  on  thia 
velocity  of  rotation,  and  therefore  greater  the  greater  the  velocity. 
The  velocity  of  rotation  is  greatest  at  the  earth'*  equatnr,  where  it 
amounts  to  1660  kilometres  per  hour,  or  nearly  half  tba  Telocity  of 
the  moon's  shadow.  Hence  the  duration  of  a  total  adlpM  may,  with- 
in the  tropics,  be  nearly  doubled  by  the  earth's  rotation.  When  all 
the  favorable  circumstance*  comUne  in  the  way  we  have  just  de- 
Bcribet^,  the  duration  of  a  total  eclipae  within  the  tropics  will  be 
about  seven  minutes  and  a  lialf.  In  our  latitude  the  maximum  du- 
ration will  be  somewhat  lea*,  or  not  Imx  from  six  minute*,  but  it  i* 
only  on  very  rare  occasions,  hardly  once  in  many  centuric*,  that  all 
these  favorable  conditions  con  be  expected  to  concur. 

Oeaaltattoa  «<  Stan  by  th*  Mean.— A  phenomenon  wliieh,  geooMt- 
rically  considered,  is  analogous  to  an  eclipae  of  the  *un  ia  the  ocmil- 
tation  of  a  star  by  the  moon.  Since  all  the  bodie*  of  the  solar  syat«M 
•re  nearer  titan  the  fixed  stars,  it  is  evident  tluit  th^  auiat  tnm 


maim 


by  the  ancient  at- 

)8eil. 

C8  from  the  occa- 
r  diameter  of  tlie 
liglit  that  such  an 
[t  may  be  of  inter- 
long  duration  of 

!  to  the  earth,  or, 
l^ular  diameter  as 

listance  from  the 
meter  will  be  the 
'  June;  bence  the 
duration  is  in  the 
igee  and  also  be- 
ide  of  the  perigee 
if  Ibe  sun  at  the 
longitude  of  the 

er  that  the  centra 
son  of  this  condl> 
!  considerably  in- 
re  have  seen  that 
ward  east  with  a 
the  earth  rotates 
observer  on  the 
spending  on  this 
ater  the  velocity, 
equator,  where  it 
U  the  Telocity  of 
KdlpMmay,  wiih- 
■tioo.  When  all 
re  have  just  de- 
e  tropics  wiU  be 
ke  maximum  du- 
linutes,  but  it  is 
enturics,  that  all 
r. 

1  which,  geomat- 
sun  is  the  ooeui- 
the  solar  tymim 


SCLtPSm  Of  THE  SUN  AND  MOON. 


141 


time  to  time  pass  between  us  and  tlie  stars.  The  planets  are,  how- 
ever,  80  small  that  sucl\  a  passage  is  of  very  rare  occurrence,  and 
when  it  does  happen  the  star  is  generally  so  faint  that  it  is  rendered 
invisible  by  the  superior  light  of  tlie  planet  before  the  latter  touches 
it.  But  the  moon  is  so  large  and  her  angular  motion  so  rapid  that 
she  passes  over  some  star  visible  to  the  naked  eye  every  few  days. 
Such  phenomena  are  termed  oeeuUatiotu  of  $tar»  by  the  moon.  It 
must  not.  however,  l»e  supposed  that  tliey  can  be  observed  by  the 
naked  eye.  In  general,  the  moon  is  so  bright  that  only  stars  of  the 
first  magnitude  can  be  seen  in  actual  contact  with  her  limb,  and  even 
then  the  contact  must  be  with  the  unilluminated  limb. 


OHAfTDK  IX. 


l!:-l 


THE  EARTH. 

Our  object  in  the  present  cliaptcr  is  to  trace  tlie  efiFects 
of  terrestrial  gravitation  and  to  study  the  changes  to  which 
it  is  srbject  in  various  places.  Since  every  part  of  the 
earth  attracts  every  other  part  as  well  as  every  object  upon 
its  surface,  it  follows  that  the  earth  and  all  the  objects 
that  we  consider  terrestrial  form  a  sort  of  system  by  them- 
selves, the  parts  of  which  are  firmly  bound  together  by 
their  mutual  attraction.  This  attraction  is  so  strong  that 
it  is  found  impossible  to  project  any  object  from  the  sur- 
face of  the  earth  into  the  celestial  spaces.  Every  particle 
of  matter  now  belonging  to  the  earth  must,  so  far  as  we 
can  see,  remain  upon  it  forever. 


Mam  avd  Biviitt  or  tex  Eaktk. 

The  mass  of  a  body  may  be  defined  as  the  quantity  of 
matter  which  it  contains. 

There  are  two  ways  to  measure  this  quantity  of  matter:  (1)  By 
the  attraction  or  weight  of  the  body— this  weiglit  being,  in  fact,  the 
mutual  force  of  attraction  between  the  body  and  the  earth ;  (2)  By 
the  inertia  of  the  body,  or  the  amount  of  force  which  we  must  apply 
to  it  in  order  to  nuke  it  move  with  a  definite  velocity.  Mathemati- 
cally, Uiere  is  no  reason  why  these  two  methods  should  give  the  same 
result,  but  by  experiment  it  is  found  that  the  attraction  of  all  bodies 
is  proportional  to  their  inertia.  In  other  words,  all  bodies,  whatever 
their  chemical  constitution,  fall  exactly  the  same  number  of  feet  in 
one  second  under  the  influence  of  gravity,  supposing  them  in  a 


0  trace  tlie  effects 

1  changes  to  which 
every  part  of  the 
every  object  upon 
Dd  all  the  objects 
)f  system  by  them- 
K>und  together  by 
1  is  so  strong  that 
ject  from  the  sur- 
8.  Every  particle 
Qust,  80  far  as  we 


Eastk. 

us  the  quantity  of 


ty  of  matter:  (1)  By 
lit  being,  in  fact,  tbe 
id  tlie  eartli;  (2)  By 
whicli  we  must  apply 
elocity.  Mathemati- 
sliould  give  tbe  same 
traction  of  all  bodies 
,  all  bodies,  whatever 
ae  number  of  feet  in 
apposing  them  in  • 


THE  EARTH. 


148 


vacuum  and  at  the  same  place  on  the  earth's  surface.  Although  the 
mass  of  n  body  is  most  conveniently  measured  by  its  weight,  yet 
mass  and  weiglit  must  not  be  confounded. 

The  weight  of  a  body  is  the  apparent  force  with  which  it 
is  attracted  toward  the  centre  of  the  earth. 

This  force  is  not  the  same  in  all  parts  of  the  earth,  nor  at  dif- 
ferent beiglits  above  the  earth's  surface.  It  is  therefore  a  variable 
quantity,  depending  upon  the  position  of  the  body,  while  tbe  mass 
of  the  body  is  sometliing  inherer'  <n  it,  wliich  remains  constant 
wherever  the  body  may  .    tak  an  if  it  is  carried  through  tbe 

celestial  spaces,  where  V      -^ight  fr      ■'be  reduced  to  almost  i.ui.. 

ing. 

The  unit  of  mass  which  we  may  adopt  is  arbitrary.  Qenerally  the 
most  convenient  unit  is  the  weight  of  a  body  at  some  flaed  place  on 
the  earth's  surface— the  city  of  Washington,  for  example.  Suppose 
wc  tiike  such  a  portion  of  the  earth  as  will  weigli  one  kilogramme  in 
Wnshiiigton;  we  may  then  consider  the  moss  of  that  particular  lot  of 
earth  or  rock  ns  tbe  unit  of  mass,  no  matter  to  what  part  of  the  uni- 
verse we  take  it.  Suppose,  also,  that  we  could  bring  all  the  matter 
composing  the  earth  to  tlie  city  of  Washington,  one  unit  of  mass  at 
a  time,  for  tlie  purpose  of  weighing  it,  returning  each  unit  of  mass  to 
its  pUice  in  the  earth  immediately  after  weighing,  so  that  there  should 
be  no  disturbance  of  the  earth  itself.  Tlie  sum-toUl  of  the  weights 
thus  f«»«nd  would  be  the  mass  of  the  earth,  and  would  be  a  perfectly 
definite  quantity,  admitting  of  being  expressed  in  kilogrammes  or 
pounds.  We  can  readily  calculate  the  mass  of  a  volume  of  water 
equal  to  that  of  the  earth  because  we  know  the  magnitude  of  the 
earth  in  litres,  and  the  mass  of  one  litre  of  water.  Dividing  this 
into  the  mass  of  the  earth,  supposing  ourselves  able  to  determine 
this  mass,  and  we  shall  have  the  specific  gravity,  or  what  is  more 
properly  called  the  density,  of  the  earth. 

What  we  have  supposed  for  the  earth  we  may  imagine  for  any 
heavenly  body ;  namely,  that  it  is  brought  to  the  city  of  Washington 
in  small  pieces,  and  there  weighed  one  piece  at  a  time.  Thus  the 
total  mass  of  the  earth  or  any  heavenly  body  is  a  perfectly  defined 
and  determinate  quantity. 

It  may  be  remarked  in  this  connection  that  our  units  of  weight,  tbe 
pound,  the  kilogramme,  etc.,  are  practically  unite  of  mass  rather  than 
of  weight.  If  we  should  weigli  out  a  pound  of  tea  ia  the  latitude  of 
Washington,  and  then  take  it  to  tbe  equator,  it  would  really  be  less 
hwvy  at  the  equator  thao  in  Washington ;  but  U  w»  t«]i»  «  prao^ 


14i 


ASTRONOMT. 


i'M 


weight  with  us,  that  a1i<.  sultl  be  lighter  at  the  equator,  lo  that  the 
two  would  still  balance  eaoh  otiier,  and  the  ten  would  Ite  still  con- 
sidered lis  weighing  one  pound.  Since  tilings  are  actually  weighed 
in  this  way  by  weights  wliich  weigh  one  unit  at  some  definite  place, 
say  Washington,  and  which  are  carried  ail  over  the  world  without 
being  changed,  it  follows  that  a  body  which  has  any  given  weight  in 
one  place  will,  as  measured  in  this  way,  liave  the  same  apparent 
weiglit  in  any  otlier  pfau»,  bough  its  real  weight  will  Tary.  But 
if  a  spring-balance  or  any  other  instrument  for  dcterminmg  abaolute 
weights  were  adopted,  tlien  we  ahould  And  that  the  weight  of  the 
same  body  varied  as  we  tfiolc  it  from  one  part  of  the  earth  to  another. 
Since,  however,  we  do  not  use  this  sort  of  an  instrument  in  weigh- 
ing, but  pieces  of  metal  which  are  carried  about  without  change,  it 
follows  that  what  we  call  units  of  weiglit  are  properly  units  of  mass. 
Density  ef  the  larth.— We  see  that  all  bodies  around  ua  tend  to  fall 
toward  the  cenire  of  the  earth.  According  to  the  law  of  gravitation, 
tills  tendency  is  not  simply  a  single  force  directed  toward  the  centre 
of  tlie  earth,  but  is  the  resultant  of  an  infinity  of  separate  forces 
arising  from  the  attractions  of  all  the  separate  parts  which  compose 
the  earth.  The  question  may  arise,  how  do  we  know  that  each 
particle  of  the  eartii  attracts  a  stone  which  falls,  and  that  the  whole 
attraction  does  not  reside  in  thn  centre  ?  The  proofs  of  this  are 
numerous,  and  consist  ratlier  in  the  exactitude  with  which  the 
tiieory  represents  a  great  mass  of  disconnected  phenomena  than  in 
any  one  principle  admitting  of  demonstration.  Perhaps,  however, 
tiie  most  conclusive  proof  is  found  in  the  hbeerved  fact  that  maaaea 
of  matter  at  the  surface  of  tlie  earth  do  really  attract  each  other  aa 
required  by  tlifr  li  of  Nbwton.  It  is  found,  for  example,  that 
isoluted  mountain*       -act  a  plumb-line  in  their  neighboriiood. 

It  is  notoworthj  that  though  aitronomy  affords  ns  the 
means  of  determinitig  with  great  precision  the  relative 
masses  of  the  earth,  the  moon,  and  all  the  planets,  it  does 
not  enable  as  to  determine  the  absolute  mass  of  anj  'lea- 
Tenly  body  in  units  of  the  weights  we  use  on  the  earth. 
The  sun  has  about  3;i8,000  times  the  mass  of  the  earth,  and 
the  moon  only  ^  of  this  mass,  but  to  know  the  abwdute 
mass  of  either  of  them  we  must  know  how  many  kilo- 
grammes of  matter  the  earth  oontains.  To  determine  this 
we  must  know  the  meM  density  of  the  enrth,  tnd  thii  is 


■iirii«i  I  ■■..tiw^inhn 


.mmiumii 


THE  KARTH. 


140 


equator,  lo  that  the 

would  lie  8tni  con- 
re  actually  weighed 
some  deflnite  place, 
■  the  world  without 
any  given  weight  in 

tiie  ume  apparent 
ght  will  vary.  But 
leterniining  abaolute 
t  the  weight  of  the 
the  earth  to  another. 
Dstrument  in  weigh- 
t  without  change,  it 
iperly  units  of  maaa. 
round  us  tend  to  fall 
9  law  of  graTitation, 
d  toward  the  centre 
f  of  separate  forces 
arts  which  compose 
ve  know  that  each 

and  that  the  whole 
9  proofs  of  this  are 
le  with  which  the 
piienomena  than  in 

Perhaps,  howerer, 
red  fact  that  masses 
ttract  each  other  as 
I,  for  example,  that 
leighboriiood. 

ly  affords  ns  the 
Bion  the  relative 
e  planeta,  it  does 
maaa  of  any  'lea- 
ise  on  the  earth. 

of  the  earth,  and 
now  the  abadnte 

how  many  kilo- 
Fo  determine  this 
ewrth,  and  thii  is 


something  about  which  direct  observation  can  give  us  no  in- 
formation, because  wo  cannot  penetrate  more  thun  un  in- 
significant distance  into  the  earth's  interior.  The  only  way 
to  determine  the  density  of  the  earth  is  to  fltid  how  much 
matter  it  must  contain  in  order  to  attract  bodies  on  its  tiur- 
fuce  with  a  force  equal  to  their  observed  weight ;  tliut  is.  with 
such  intensity  thut  at  the  equator  a  body  shall  fall  nearly 
five  metres  in  a  second.  To  find  this  we  must  know  the 
relation  between  the  mass  of  a  body  and  its  attractive 
force.  This  relation  can  only  bo  found  by  measuring  the 
attraction  of  a  body  of  known  mass. 

An  attempt  to  do  tliis  was  made  toward  the  close  of  the  last  cen- 
tury, the  attracting  bo<ly  selected  being  Mount  Scheliallien  in  Scot- 
land. The  volume,  F,  of  the  mouiilain  was  linown  by  careful  topo 
graphical  surveys.  The  specific  gravUv  or  density,  2>,  of  the  rocks 
composing  the  mountain  was  determined  by  experiment.  The  mass, 
M,  of  the  mountain  was  VxD;  that  is,  a  known  quantity. 

A  plumb-line  set  up  at  the  south  end  of  the  mountain  wab  attrucled 
away  from  the  true  vertical  toward  the  mountain;  that  is,  toward 
the  north.  A  plumb-line  at  the  north  end  of  the  mountain  was 
attracted  toward  the  south.  The  amounts  of  these  deviations  were 
measured,  and  they  ^/ere  due  to  the  muss  of  the  mountuio.  Hence  a 
measure  of  Its  attractive  force  was  obtained. 

The  actual  process  of  determining  the  deviations  of  the  plumb- 
lines  y  and  5  was  this:  The  latitude  of  the  stations  8md  Nvien 
determined.    These  were  nothing  but  the  decliuations  of  the  xenitlu  . 
of  Jfand  8,  the  seniths  being  determined  by  the  directions  of  plumb- 
lines  at  each  station.    The  difference  of  latitudes  of  N  and  8  by  ^ 
astronomiml  observations  was  known  in  arc  and  therefore  in  feet 
If  the  mountain  had  no  attraction  on  the  plumb-lines,  this  differ 
ence  in  feet  would  be  the  same  as  the  distance  apart  of  the  two 
stations  determined  by  tlie  topt^rnphical  survey.    But  it  was  differ- 
ent and  the  amount  of  the  difference  was  a  measure  of  the  attraction 
of  this  particular  mass.    This  is  the  general  principle  according  to 
which  the  relation  of  mass  and  attraction  ia  determined.  As  the  mass 
of  the  mountain  and  its  attraction  was  known,  the  density  of  the 
wliole  earth  ooald  he  determined.    The  earth's  maaa  (M')  was  equal- 
to  IW  TOh»ii0  i  V)  i\m»\f  density  (2)').    {to  yolwne  was  known,  its 


I'ii 


146 


A8TR0N0MT. 


nam  wu  known,  bacMin  it  miut  be  nich  h  to  tttnust  bodi«  with 
forcM  measured  by  tlieir  weights,  and  hence  iu  density  wu  deter- 
mined from  this  experiment.  The  actual  result  was  that  the  earth 
waa  4*7  times  as  dense  as  water.  Otiier  researches  give  about 
5-6  for  the  density  of  the  earth;  this  is  more  than  double  the  average 
specific  gravity  of  the  roclis  which  compose  the  surface  of  the  globe: 
whence  It  follows  that  the  inner  portions  of  the  earth  are  much  more 
danae  than  the  outer  parts. 

LAWI  OV  TimUSTUAL  OlATITATIOV. 

The  earth  being  very  nearly  spherical,  certain  theorems  respecting 
the  attraction  of  splieres  may  be  applied  to  it.  The  demonstrution 
of  these  theorenu  requires  the  use  of  the  Integral  Calculus,  and  will 
be  omitted  here,  only  the  conditions  and  the  results  Iwing  stated. 
Let  us  imagine  a  hollow  shell  of  matter,  of  which  the  internal  and 
eitemal  surfacea  are  both  spheres,  attracting  any  other  mass  of 
matter,  a  small  particle  we  may  suppose.  This  particle  will  be 
attracted  by  every  particle  of  the  shell  with  a  force  inversely  as  the 
square  of  iU  distance  from  it.  The  total  attraction  of  the  shell  will 
be  tlie  resultant  of  this  inflnity  of  separate  attractive  forces. 

Thkorkm  I.— If  th»  particle  be  tmteide  the  ahell,  it  will  be  attraeied 
a$iftke  vhole  moM  </  Oie  tkett  were  eoneentrated  in  ite  centre. 

Thborrm  II.— (T  '^  particle  be  I'nstdt  the  ehell,  tJie  oppotOe  aUrae- 
tione  in  eterji  direction  vHu  neutraliMe  each  other,  no  tnatter  vltcreabmtte 
in  the  interior  the  particle  majr  be,  and  the  reeultant  attraction  of  the 
iheU  wiU  thenfore  be  uro. 

To  apply  this  to  the  attraction  of  a  solid  sphere,  let  us  first  8up> 
pose  a  body  either  outside  the  sphere  or  on  its  aurface.  If  we  con- 
oalT«  tlie  apbeie  as  made  up  of  a  great  number  of  spherical  shells,  the 

attracted  point  will  be  external  to  ail  of 
them.  Since  each  ahell  attracts  as  if 
its  whole  mass  were  in  the  cent.e,  it 
follows  that  the  whole  sphere  attracts 
a  body  upon  the  outaide  of  ita  surface 
as  if  its  entire  maaa  were  concentrated 
»;  its  centre. 

Let  us  sow  uappom  the  attracted 
particle  inaide  the  splien,  as  at  P,  Fig. 
45.  and  imagine  a  spherical  surface 
FQ  oonoantric  with  the  sphere  and 
paaalng  tbrouf^  the  attraeted  particle. 
f|a^  ^  4k\\  that  p«rtio«i  of  the  sphere  lyiaf' 


Mnci  bodlM  with 
density  wu  deter- 
HTM  that  the  ewtb 
ircbes  glTe  ftbout 
louble  the  average 
rface  of  the  globe: 
rth  are  much  more 


.TIOV. 

leorems  respecting 
riie  demonstmtion 
Calculus,  and  will 
>ults  being  stated. 
1  the  internal  and 
ny  other  mass  of 
s  particle  will  be 
ee  inversely  aa  the 
m  of  the  shell  will 
ve  forces. 
it  will  be  attraeUd 
itt  centre, 
the  opponte  attrat' 
matter  whereaboufe 
nt  attraetion  of  tK* 

«,  let  us  first  sup- 
irface.  If  we  con- 
ipherical  shells,  the 
«  external  to  all  of 
ibell  attracts  as  if 
I  in  the  centic,  it 
ole  sphere  attracts 
taide  of  its  surface 
irere  concentrated 

MM  the  attracted 
)heie,  M  at  P,  Fig. 

spherical  surface 
h  the  sphere  and 
attracted  particle. 

tlie  sphere  lyiaf^ 


THK  EARTH. 


147 


geometry,  4  )r^-    Dividing  by  the  square  of  the  distance  r,  wo  see 
8 


ouUide  this  spherical  surface  will  be  a  uphcrical  shell  having  thn 
particle  Inside  of  It,  and  will  therefore  exert  no  iitiractioii  whntever 
on  the  particle.  That  portion  inside  the  surfnce  will  constitute  n 
sphere  with  the  particle  on  its  siirfnco,  nnd  will  therefore  attract  ns 
if  all  this  portion  were  concentrated  in  the  centre.  To  flnil  what 
this  attraction  will  be,  let  us  lirst  suppose  the  whole  sphere  of  equal 
density.    Let  us  put 

a,  the  radius  of  the  entire  sphere. 

r,  the  distance  PCot  the  particle  from  the  centre. 

TlietoUl  volume  of  matter  inside  the  splicre  PQ  will  then  be,  by 

geometry,-5)rr*.    Dividing  by  the  squan 
o 

that  the  attraction  will  be  represented  by 

4 

that  is.  inside  the  sphere  tlfe  attraction  will  be  directly  as  the  dis- 
tance of  the  particle  from  the  centre.     If  the  |Hirticle  is  at  the  sur- 

4 
face  we  have  r  =  a,  and  the  attraction  is  -^  na.    Outoide  tiie  sur- 
face the  whole  volume  of  the  sphere  -g  «  «'  will  attract  the  particle, 

4      a* 
and  the  attraction  will  be  ^  «  -:.   If  we  put  r  =  o  in  this  formula, 

o        I 

we  shall  have  the  same  result  as  before  for  the  surface  attraction. 

Let  us  next  suppose  that  the  density  of  the  sphere  varies  from  its 
centre  to  its  surface,  so  as  to  lie  equal  at  equal  distances  from  tlie 
centre.  We  may  then  conceive  of  it  as  formed  of  an  infinity  of  con- 
centric spherical  shells,  each  homogeneous  in  density,  but  not  of  the 
same  density  as  the  others.  Tlieoreros  I.  and  II.  will  then  still 
apply,  but  their  result  will  not  be  the  same  t»  in  the  case  of  a  homo- 
geneous sphere  ior  a  particle  inside  the  sphere.  Referring  to  Tig. 
45,  let  w  put 

D,  tlie  mean  density  of  the  shell  outside  the  particle  P. 
2)*,  the  mean  density  of  the  portion  P  Q  inside  of  P. 

We  shall  then  hav« : 

Volume  of  the  shell,  4  '  (a*  —  r*)-    Volume  of  the  inner  nphera, 
8 

int*.    Mas^  pf  the  sh9ll  =  vol.  X  Z>  =  4  »  i)  (a»  —  r»).    Mass  of  the 


141 


ASTROJfOMfT. 


: 


MaM 


inner  •?«««  =  ▼ol.  x  I^  =»  J-  *  ffr*.     Mnu  of  the  whoU  iplwra  = 

•U!n  of  moMOi  it  •hell  »nd  Inner  sphere  ■  jj-  «  (  />  a»  +  (D"  -  U)  H|i 
Attraciion  of  the  whole  iphere  upon  »  point  M  lU  lurfhce  ■ 

Attraction  of  tlio  inner  ipliere  (Ihe  mne  Mthat  of  the  Whole  iheU) 

_     Mkm     4  ^  „. 

upon  »  point  at  i*  = -^- =  g- « ■t' ^ 

If,  OS  in  tlie  awe  of  the  earth,  the  density  continually  Increases  to- 
ward the  centre,  the  Tnlue  of  Df  will  increase  adto,  as  r  diminislies,  so 
that  gravity  will  dlininlsli  less  rapidly  than  In  the  case  of  a  home 
ffeneous  sphere,  and  may.  in  fact,  actually  Increase  as  we  descend. 
To  show  this,  let  us  suhlract  the  attraction  at  Pfrom  that  at  the  sur. 
face.    The  difference  will  give  : 

Diminution  at  P  =  J^  «  (^a  +  (D* - 2>)  -,- iXr ^ 

Kow  let  us  suppose  r  a  very  little  less  than  a,  and  put  r  =«  a  -rf; 
d  will  then  Im  the  depth  of  the  particle  below  the  surface. 
Cubing  this  value  of  r,  neglecting  the  higher  powen  of  0,  and 

dividing  by  a«,  we  find  ^  =  a  -8d.     SubatltuUng  in  the  above 

equation,  the  diminution  of  gravity  at  P  beeomes  3  « (82)  -VD^i. 

We  see  that  if  8  D  <  3  /)'— that  is.  If  the  density  at  the  surfuce  is 
less  tlw"  I  of  the  mean  density  of  the  whole  Inner  mass— this  quan- 
tlty  will  become  negative,  showing  that  the  force  of  gravity  will  be 
less  at  the  surfuoe  than  at  a  small  depth  in  the  interior.  But  it  must 
ultimately  diminish,  because  it  is  neoesMirily  «ero  at  the  centre.  It 
was  on  this  principle  that  Profesaor  Airt  determined  the  density  of 
the  earth  by  comparing  the  vibrations  of  a  pendulum  at  the  bottom 
of  the  Harton  Colliery,  and  at  the  surface  of  the  earth  in  the  neigh- 
borhood. At  the  bottom  of  the  mine  the  pendulum  gained  about 
2'-5  per  day,  showing  the  foroe  of  gravity  to  be  greater  there  than  at 
the  surface. 

Fraou  AiB  Kijonnnxi  ov  no  Iaihl 

If  the  earth  were  fluid  and  did  not  rotate  on  its  axis,  it 
would  auiume  the  form  of  a  perfect  sphere.    The  opinioQ 


irhoto  iphtra  a 

+  (/)'- iDf*)i 
t  iu  turflwfl  m 

Ui«  whole  sbell) 


My  inereMM  to* 
r  dimiDisliM,  w 
CBM  of  a  homo, 
u  we  deacend. 
I  Uut  at  the  aur- 


-^ 


Dfry 


i  put  r  St  a  —  rf; 

rface. 

owen  of  d,  and 

g  in  the  above 

at  the  lurfiice  ii 
mau — thii  quan- 
f  gravity  will  be 
lor.  But  it  muat 
It  the  centre.  It 
Bd  the  density  of 
tm  at  the  bottom 
uth  in  the  neigli- 
iim  gained  about 
ater  thexe  tban  at 


)  on  ita  axis,  it 
,    The  opinioQ 


TUK  EARTH. 


149 


is  entertained  that  the  earth  was  once  in  a  molten  state, 
and  that  this  is  the  origin  of  ita  present  nearly  spherical 
form.  If  we  give  such  a  sphere  a  rotation  upon  its  axis, 
the  centrifugal  force  at  the  equator  acts  in  a  direction  op- 
posed to  gravity,  and  thus  tends  to  enlarge  the  circle  of 
the  equator.  It  is  found  by  mathematical  analysis  that  the 
form  of  such  a  revolving  J9uid  sphere,  supposing  it  to  be 
perfectly  homogeneous,  will  be  an  oblate  ellipsoid  ;  that  is, 
all  the  meridians  will  be  equal  and  similar  ellipses,  having 
their  major  axes  in  the  equator  of  the  sphere  and  their 
minor  axes  coincident  with  the  axis  of  rotation.  Onr  earth, 
however,  is  not  wholly  fluid,  and  the  solidity  of  its  conti- 
nents prevents  its  assuming  the  form  it  would  tn  9  if  the 
ooeiui  covered  its  entire  surface.  By  the  figure  of  the 
earth  we  mean,  hereafter,  not  the  outline  of  the  solid  ani 
liquid  portions  respectively,  but  the  figure  which  it  would 
assume  if  its  entire  surface  were  an  ocean.  Let  us 
imagine  canals  dug  down  to  the  ocean  level  in  every  direc« 
tion  through  the  continents,  and  the  water  of  the  ocean  to 
be  admitted  into  them.  Then  the  onrved  surface  toaohing 
the  water  in  all  those  canals,  and  coincident  with  the  sur- 
face of  the  ocean,  is  that  of  the  ideal  earth  considered  by 
astronomers.  By  the  figure  of  the  earth  is  meant  the  figure 
of  this  liquid  surface,  without  reference  to  the  inequalities 
of  the  solid  surface. 

We  cannot  Hty  that  this  ideal  earth  is  a  perfect  ellipsoid, 
because  we  know  that  the  interior  is  not  homogeneons,  but 
all  the  geodetic  measures  heretofore  made  are  so  nearly 
represented  by  the  hypothesis  of  an  ellipsoid  that  the  lat- 
ter is  a  very  close  approximation  to  the  true  figure.  The 
deviations  hitherto  noticed  are  of  so  irreguk  ^  oharaoter 
that  they  have  not  yet  been  reduced  to  anj  •:  ;  uun  Ikw, 


160 


ASTBONOMT. 


The  largest  which  have  been  observed  seem  to  be  due  to 
the  attraction  of  mountains,  or  to  inequalities  in  the  den> 
sity  of  the  rocks  beneath  the  surface. 

Method  of  Triangulation. — Since  it  is  practically  impossi- 
ble  to  measure  around  or  through  the  earth,  the  magnitude 
as  well  as  the  form  of  our  planet  has  to  be  found  by  com- 
bining measurements  on  its  surface  with  astronomical  ob- 
servations. Even  a  measurement  on  the  earth's  surface 
made  in  the  usual  way  of  surveyors  would  be  impracticable, 
owing  to  the  intervention  of  mountains,  rivers,  forests,  and 
other  natural  obstacles.  The  method  of  triangulation  is 
therefore  universally  adopted  for  measurements  extending 
over  largo  areas. 


(Ill, 


li 


;lii 


'■;■''■■ 


¥\ 


Vta.  it^.-~k.  Pi«r  or  nn  Twaaawi  Tbiamwilatioii  ikak  Pasis. 


Triangulation  is  executed  in  the  following  way :  Two  points,  a 
and  b,  a  few  miles  apart,  are  selected  as  tlie  extremities  of  a  base- 
line. They  must  be  so  chosen  that  their  di>tnnce  apart  can  be  accu- 
rately measured  by  rods ;  the  intervening  ground  should  therefore 
be  as  level  and  free  from  obstruction  as  possible.  One  or  more  ele- 
vated points,  E  F,  etc.,  must  be  visible  from  one  or  Iwth  ends  i>i  the 
baae-lins.  By  means  of  a  theodolite  and  by  observation  of  the  pole- 
star,  the  directions  of  these  points  relative  to  the  meridian  are  accu- 
rately observed  from  each  end  of  the  base,  as  is  also  the  direction  ab 
of  the  base-line  itself.  Suppose  .J^*  to  be  a  point  visible  from  each 
end  of  tbe  base.  th«ii  iq  the  tria:igle  abFyie  have  the  len(;th  ab^ 


THB  EAllTH. 


Iffl 


to  be  dae  to 
B  in  the  den- 

cally  impossi- 
lie  magnitude 
Dund  by  com- 
'onomical  ob- 
irth's  surface 
mpracticable, 
i,  forests,  and 
angulation  is 
ats  extending 


BAB  Pahs. 


:  Two  points,  a 
mities  of  a  base- 
Kirt  can  be  accu- 
should  therefore 
One  or  more  ele- 
Imtb  ends  o;  the 
ition  of  the  pole- 
eridian  are  accu- 
>  the  direction  a  6 
'iaible  from  each 
the  length  a  (dfh 


termined  by  actual  measurement,  and  the  angles  at  a  and  h  deter- 
mined by  observations.  With  these  data  the  lengths  of  the  sides 
ai^aud  b  Faxe  determined  by  a  simple  computation. 

The  observer  tlien  transports  his  instruments  to  F,  and  determines 
in  succession  the  direction  of  tlie  elevated  points  or  hills  D  EOHJ, 
etc.  He  next  goes  in  succession  to  each  of  these  hills,  and  determines 
the  direction  of  all  the  others  which  are  visible  from  it.  Thus  a  net- 
work of  triangles  is  formed,  of  which  all  the  angles  are  observed 
with  the  theodolite,  while  the  sides  are  successively  calculated  from 
the  first  base.  For  instance,  we  have  just  shown  how  the  side  aFia 
calculnted;  this  forms  a  base  for  the  triangle  EFa,  the  two  remain- 
ing sides  of  which  are  computed.  The  side  ^^forms  the  base  of 
the  triangle  O  EF,  tlv  sides  of  which  are  calculnted,  etc.  In  this 
operation  more  angles  are  observed  than  are  theoretically  necessary 
to  ciilculatc  the  triangles.  This  surplus  of  data  serves  to  insure  the 
detectiua  of  any  errors  in  the  measures,  and  to  test  their  accura«-y  by 
tlie  agreement  of  their  results.  Accumulating  errors  are  further 
guarded  against  by  measuring  additional  sides  from  time  to  time  as 
opportunity  offers. 

Chains  of  triangles  have  thus  been  measured  in  Russia  and  Sweden 
from  the  Danube  to  the  Arctic  Ocean,  in  England  and  France  from 
the  Hebrides  to  Algiers,  in  this  country  down  nearly  our  entire  At- 
lantic coast  and  along  the  great  lakes,  and  through  shorter  distances 
in  many  other  countries.  An  cast  and  west  line  is  now  being  run 
by  tlie  Coast  Survey  from  tiie  Atlimtic  to  the  Pacific  Ocean.  Indeed 
it  may  be  expected  tliat  a  network  of  triangles  will  be  gradually  ex- 
tended over  the  surface  of  every  civilized  country,  in  order  to  con- 
struct perfect  maps  of  it. 

Suppose  that  we  take  two  stations,  a  and  j,  Fig.  46,  situated  north 
and  south  of  each  other,  determine  the  latitude  of  each,  and  calculate 
the  distance  between  them  by  means  of  triangles,  as  in  the  figure. 
It  is  evident  that  by  dividing  the  distance  in  kilometres  by  the  dif- 
ference of  latitude  in  degrees  we  shall  have  the  length  of  one  degree 
of  latitude.  Then  if  the  earth  were  a  sphere,  we  should  at  once  hare 
its  circumference  by  multiplying  the  length  of  one  degree  by  860. 
It  is  thus  found  that  the  length  of  a  degree  is  a  little  more  than  111 
kilometres,  or  between  69  and  70  English  statute  miles.  lU  circum- 
ference is  therefore  about  40,000  kilometres,  and  its  diameter  between 
13,000  and  18,000.*  

*  When  the  metric  syBtem  was  originally  dMisned  by  the  Vyencb,  It  was  in- 
tended tliat  the  kUometi*  should  be  nin  of  Um  dlitaiice  tram  the  pole  ot  the 
earth  to  the  eqnator.  This  would  make  a  degree  of  the  meridian  eqaal,  on  Hw 
avwage.  to  XUk  UlomMtwa.  But  the  metre  aottiaUy  adfl|)taa  Is  vimAj^lA 
•BlnchtboitadM. 


Iftd 


AstnoKOitT. 


Owing  to  the  ellipticity  of  the  earth,  the  length  of  one  degree 
varies  with  the  latitude  and  the  direction  in  which  it  is  measured. 
The  next  step  in  the  order  of  accuracy  is  to  find  the  mngiiitude  and 
the  form  of  the  earth  from  measures  of  long  arcs  of  latitude  (and 
sometimes  of  longitude)  made  in  different  regions,  especially  near 
the  equator  and  in  high  latitudes.  But  we  shall  still  find  that  dif- 
ferent combinations  of  measures  give  slightly  different  results,  both 
for  the  magnitude  and  the  ellipticity,  owing  to  the  irregularities  in 
the  direction  of  attraction  which  we  have  already  described.  The 
problem  is  therefore  to  find  what  ellipsoid  will  satisfy  the  measures 
with  the  least  sum-total  of  error.  New  and  more  accurate  solutions 
will  be  reached  from  time  to  time  as  geodetic  measures  are  extended 
over  a  wider  area.    The  following  are  among  the  most  recent  results: 


Fm.47. 

the  ear  til's  polar  semidiameter,  6855  •  370  kilometres;  earth's  equatorial 
■emidiameter,  6877>877  kilometres  ;  earth's  compreesion,  ^^.^  of  the 
equatorial  diameter ;  earth's  eccentricity  of  meridian,  0'06819.  An- 
other result  is  that  of  Captain  Clarkb  of  England,  who  found: 
polar  semidiameter,  685((>459*  kilometres;  equatorial  semidiameter, 
6S78-191  kilometres. 

Oeegiapkle  aad  Oassentrie  latitodMi.— An  obvious  result  of  the 
ellipticity  of  the  earth  is  that  the  plumb-line  does  not  point  toward 
the  earth's  centre.  Let  Fig.  47  lepreaent  a  meridional  section  of  the 
earth,  N8  being  the  axis  of  rotation,  B  Q  the  plane  of  the  equator, 
and  0  the  position  of  the  observer.    The  line  HS,  tangent  to  the 

*  Captain  Clabxb's  remlU  are  glren  in  f«et.  the  polar  radiiM  toinK  ao,8B4,MS 
fset,  the  eqnatorial  aa,8l6,aoiL    These  numbers  are  in  the  praportlM  MB  :«i. 


of  one  degree 
it  is  measured, 
magnitude  nod 
f  latitude  (and 
especially  near 
1  find  that  dif- 
»t  results,  both 
rregularities  in 
escribed.  The 
y  the  measures 
!urnte  solutions 
>s  are  extended 
(recent  results: 


J 


Tax  SAJiTB. 


158 


«arth  at  0,  will  then  jreprescnt  the  horizon  of  the  obserrer,  while  the 
line  Z  If',  perpendicular  to  HB,  and  therefore  normal  to  the  earth 
•Jit  0.  will  be  ihe  verlioul  as  determined  by  the  plumb-line.  The  angle 
OJf'Q,  or  ZO  Q',  which,  the  observer's  zenith  makes  with  the  equa- 
tor will  then  be  his  astronomical  or  geographical  latitude.  This  is 
the  latitude  which  in  practice  we  always  have  to  use,  because  we 
are  obliged  to  determine  latitude  by  astronomical  observation,  and 
not  by  measurement  from  the  equator.  We  cannot  determine  the 
direction  of  the  true  centre  C  of  the  earth  by  direct  observation  of 
any  kind,  but  only  the  direction  of  the  plumb-line,  or  of  the  perpen- 
dicular to  A  fluid  surface.  ZOQ  is  the  astronomical  latitude.  If, 
however,  we  conceive  the  line  COt  drawn  from  the  centre  of  tlie 
earth  Uirougli  0,  z  will  be  the  observer's  geoeentrie  tmith,  while  the 
angle  O  C  Q  will  be  his  geoeentrie  latitude.  It  will  be  observed  that  it 
is  the  geocentric  and  nottlie  geographic  latitude  which  gives  the  true 
position  of  tlie  observer  relative  to  the  earth's  centre.  The  difference 
between  tlic  two  latitudes  is  the  angle  CON'  otZOt;  this  is  called 
tlic  angle  of  tlie  vertical.  It  is  zero  at  the  poles  and  at  the  equator,  be- 
ouise  hero  the  normals  pass  through  the  centre  of  the  ellipse,  and  it 
attains  its  mnximnm  of  11'  80"  at  latitude  46°.  It  will  be  seen  that  the 
geocentric  latitude  is  always. less  than  the  geographic.  In  north 
latitudes  the  geocentric  zenith  is  south  of  the  apparent  zenith,  and  in 
southern  laUtudcs  north  of  it;  being  nearer  the  equator  in  each  case. 


*f 


rth's  equatorial 
on,  f^.T  of  the 
008819.  An- 
d,  who  found: 
semidiameter, 

I  result  of  the 
it  point  toward 
I  section  of  the 
of  tlw  equator, 
tangent  to  the 


Mtknsm-.am. 


MvnuK  or  thi  lAXTtfa  Ajjm,  ob  Phomuov  or  thi 

Saunrozif. 

UdeTMl  uid  Squinoctial  Ymt.— lu^dewribing  theftppar- 
ent  motion  of  the  Bun,  two  ways  of  finding  the  time  of  its 
apparent  rerolntion  around  the  sphere  were  described;  in 
other  words,  of  fixing  the  length  of  a  year.  One  of  these 
metliods^consisU  in  finding  the  interral  between  sucoessive 
MiMgia  of  the  nm  throngih  theeqninozes,  or,  which  is  the 
,|nHBe  thing,  across  the  plane  of  the  eqnator,  and  the  other 
Iby  finding.wben  it  retnms  to  the  same  positi<m  among  the 
>tiun.  Two  thoQiand  years  ago  Hippabchub  fonnd,  by 
amfumg  his  own  obserrations  with  tho«e  made  two  cm- 
ianm  bKCeie  t^  Tumkharis,  Uuit  thoie  Ipo  -Htttltods  of 


154 


A8TB0N0MT. 


fixing  the  length  of  the  year  did  not  give  the  same  resnlt. 
It  had  previously  been  considered  that  the  length  of  a  year 
was  abont  365^  days,  and  in  attempting  to  correct  this 
period  by  comparing  his  observed  times  of  the  sun's  pass- 
ing the  equinox  with  those  of  Timocharis,  Hipparchus 
found  that  the  length  required  a  diminution  of  seven  or 
eight  minutes.  He  therefore  concluded  that  the  true  length 
of  the  equinoctial  year  was  365  days  5  hours  and  about  63 
minutes.  When,  however,  he  considered  the  return  of  the 
sun  not  to  the  equinox,  but  to  the  same  position  reUtive 
to  the  bright  star  Spica  Virginis,  he  found  that  it  took 
some  minutes  more  than  365^  days  to  complete  the  revolit- 
tion.  Thus  there  are  two  years  to  be  distinguished,  the 
tropical  or  equinoctial  year  and  the  sidereal  year.  The 
first  is  measured  by  the  time  of  the  sun's  return  to  the 
equinox;  the  second  by  its  return  to  the  same  position 
relative  to  the  stars.  Although  the  sidereal  year  is  the 
correct  astronomical  period  of  one  revolution  of  the  earth 
around  the  sun,  yet  the  equinoctial  year  is  the  one  to  be 
used  in  civil  life,  because  the  change  of  seasons  depends 
upon  that  year.  Modern  determinations  show  the  respec- 
tive lengths  of  the  two  years  t«  be : 


366">  6"    O"    9'  =  365"".25636.    ,, 
365"  S""  IS-  46"  =  365«.a4220.    , 


Sidereal  year, 
Equinoctial  year. 

It  is  evident  from  this  difference  between  the  two  yeain 
that  the  position  of  the  equinox  among  the  stars  must  be 
changing,  and  that  it  mast  mbve  toward  tiie  west,  because 
the  equinoctial  year  is  the  shorter.  This  motion  is  called 
tha  precession  of  the  equinoxes,  and  amounts  to  about  50'' 
per  year.  The  equinox  being  simply  the  point  in  which 
the  equator  and  the  ecliptic  intersect,  it  is  evident  that  it 


_ji,,^„„„tj.-.l*SI 


le  same  resnlt. 
ingth  of  a  year 

0  correct  this 
the  son's  pass- 

HlPPABCHUS 

»n  of  seven  or 
:he  true  length 
and  about  63 
)  return  of  the 
sition  reUtive 

1  that  it  took 
ite  the  revold- 
nguished,  the 
xl  year.     The 

return  to  the 
same  position 
il  year  is  the 
1  of  the  earth 
bhe  one  to  be 
tsons  depends 
>w  the  respeo* 

65"".25636.    ,, 
S5*.a4220.    , 

the  two  yeairs 
stars  must  be 
west,  because 
>tion  is  called 
to  about  50^' 
>int  in  which 
ident  that  it 


TEE  BASTE. 


166 


can  change  only  through  »  change  in  one  or  both  of  these 
circles.  Hipfarchus  found  that  the  change  was  in  the 
equator  and  not  in  the  ecliptic,  because  the  declinations 
of  the  stars  changed,  while  their  latitudes  did  not.  Since 
the  equator  is  defined  as  a  circle  everywhere  90°  distant 
from  the  pole,  and  since  it  is  moving  among  the  stars,  it 
follows  that  the  pole  must  also  be  moving  auiong  the  stars. 
But  the  pole  is  nothing  more  than  the  point  in  which  the 
earth's  axis  of  rotation  intersects  the  celestial  sphere:  the 
position  of  this  pole  in  the  celestial  sphere  depends  solely 
upon  the  direction  ot  the  earth's  axis,  and  is  not  changed  by 
the  motion  of  the  earth  around  the  sun.  Heuce  precession 
shows  that  the  direction  of  the  earth's  axis  is  continually 
changing.  Careful  observations  from  the  time  of  Uippab- 
CHCS  until  now  show  that  the  change  in  question  consists 
in  a  slow  revolution  of  the  pole  of  the  earth  around  the  pole 
of  the  ecliptic  as  projected  on  the  celestial  sphere.  The 
rate  of  motion  is  such  that  the  revolution  will  be  completed 
in  between  25,000  and  26,000  years.  At  the  end  of  this 
period  the  equinox  and  solstices  will  have  made  a  complete 
revolution  in  the  heavens. 


The  nature  of  this  motion  will  be  seen  more  clearly  by  referring  to 
Fig.  88,  p.  98.  We  have  tliere  represented  tlie  earth  in  four  poai- 
tions  during  its  annual  revolution.  We  have  represented  the  axis  as 
inclining  to  the  right  in  each  of  these  positions,  and  have  described 
il  as  remaining  parallel  to  itself  during  an  entire  revolution.  The 
phenomena  of  precession  show  that  this  is  not  absolutely  true,  but 
that,  in  reality,  the  direction  of  the  axis  is  slowly  changing.  Tbia 
change  is  such  that,  after  the  lapse  of  some  0400  years,  the  north 
pole  of  the  earth,  as  represented  in  the  figure,  will  not  incline  to  the 
ri^t,  but  toward  the  observer,  the  amount  of  the  inclination  remain* 
ing  nearly  the  same.  The  result  will  evidently  be  a  shifting  of  the 
seasons.  At  D  we  shall  have  the  winter  solstice,  because  the  north 
pole  will  be  inclined  toward  the  observer  and  tlierefon  from  the  sun, 


fA 


166 


ASTROKaur. 


'I 


while  at  A  we  sball  have  the  venial  equinox  instead  of  the  winter 
solstice,  and  so  on. 

Id  6400  years  more  the  north  pole  will  be  inclined  toward  the  left, 
and  the  seasons  will  be  reversed.  Another  interval  of  the  same 
length,  and  the  north  pole  will  be  inclined  from  the  observer,  the 
seasons  being  shifted  through  another  quadrant.  Finally,  at  the 
end  of  about  25,800  years,  the  axis  will  have  resumed  its  original 
direction. 

Precession  thus  arises  from  a  motion  of  the  earth  alone  and  not  of 
the  heavenly  bodier.  Although  the  direction  of  tlie  earth's  axis 
changes,  yet  the  position  of  this  axis  relative  to  the  crust  of  the  earth 
remains  invariable.  Borne  have  supposed  that  precession  would 
result  in  a  change  in  tlie  position  of  the  north  pole  on  the  surface  of 


I  .(. 


r».  A 


the  earth,  so  that  the  northera  i«|^ons  would  be  covered  bj  the 
ocean  as  a  result  of  the  different  direction  in  which  the  ocean  would 
be  carried  by  the  centrifugal  force  of  the  earth's  rotation.  This,  bow- 
ever,  is  a  mistake.  It  has  been  shown  that  the  position  of  the  poles, 
and  therefore  of  the  equator,  on  the  surface  of  the  earth,  cannot 
change  except  from  some  variation  in  the  arrangement  of  the  earth's 
interior.  Scientific  investigation  has  yet  shown  nothing  to  indicate 
any  probability  of  such  a  change. 

The  motion  of  precession  is  not  uniform,  but  is  subject  to  several 
small  inequalities  which  are  called  nutathn. 


TBI  Oauu  w  PuMsmov. 

The  cause  of  preoesdon,  ete.,  is  illuslratcd  in  the  flgura,  iirtMi 
shows  a  spherical  earth  surrounded  by  a  ring  of  natter  atv«b»«q||p- 
tor.  If  the  mxik  were  really  spherical  there  would  he  «o  prMN^WL 
It  is^  bosf«ver,  cUipwHdal  with  a  protubenaoe  at^lw  npi»r.  -ftht 


Bad  of  the  winter 

d  toward  the  left, 

rral  of  the  aame 

the  ohaerrer,  the 

Finally,  at  the 

lumed  its  original 

I  alone  and  not  of 
the  earth's  axis 
I  crust  of  the  earth 
precession  would 
on  the  surface  of 


le  covered  hj  the 
I  the  ocean  would 
ition.  Thi8,bow- 
lition  of  the  poles, 
the  earth,  cannot 
sent  of  the  earth's 
Dthing  to  indicate 

subject  to  aereral 


tiM  figure.  i|riM> 
i»tteratv«be«K|{|a- 
i  he  «o  pTMNsiUp. 


■-r 


TffB  SAnTH. 


vn 


effect  of  this  protuberance  is  to  be  examined.  Consider  the  action 
between  the  sun  and  earth  alone.  If  the  ring  of  matter  were  absent, 
the  earth  would  revolve  about  the  sun  as  is  shown  in  Fig.  82,  p.  98 
(Seasons). 

We  remember  that  the  sun's  N.  P.  D.  is  W  at  the  equinoxes,  and 
66i°  and  118^°  at  the  solstices.  At  the  equinoxes  the  sun  is  in  the 
direction  Cm;  that  is,  NOm  is  00°.  At  the  winter  solstice  the  sun  is 
in  the  direction  Oe;  NCe  =  113i°.  It  is  clear  that  in  the  latter  case 
the  effect  of  the  sun  on  the  ring  of  matter  will  be  to  pull  it  down 
from  the  direction  Cm  towards  the  direction  Ce,  An  opposite  effect 
will  be  produced  by  the  sun  when  its  polar  distance  is  66i°. 

The  moon  also  revolves  round  the  earth  in  an  orbit  inclined  to  the 
eqiutor.  and  in  every  position  of  the  moon  it  has  a  different  action 
on  the  ring  of  matter.  The  earth  is  all  the  time  rotating  on  its  axis, 
and  these  varying  attractions  of  sxm  and  moon  are  equalized  and 
distributed  since  different  parts  of  tlie  eartli  are  successively  presented 
to  the  attracting  body.  "The  result  of  all  the  complex  motions  we 
have  described  is  a  conical  motion  of  the  earth's  axis  JV  G  about  the 
line  CB. 

The  earth's  shape  is  not  that  given  in  the  flgtire,  but  it  is  an  ellip- 
soid of  revolution.  The  ring  of  matter  is  not  confined  to  the  equator, 
but  extends  away  from  it  in  both  directions.  Tiie  effects  of  the 
forces  acting  on  the  earth  as  it  is  are  however,  similar  to  the  effects 
we  have  described. 


CHAPTER  X. 


.  t 


lu    i 


h  « 


i*    i 


CELESTIAL  MEASUREMENTS  OF  MASS  AND  DISTANCE. 

XbB  GZUniAI  fklALE  Of  KSAnrUlCEHT. 

The  uuitB  of  length  and  mass  employed  by  astronomws 
are  necessarily  different  from  thope  used  in  daily  life.    The 
distances  and  magnitudes  of  the  heavenly  bodies  are  never 
reckoned  in  miles  or  other  terrestrial  measures  for  astro- 
nomical purposes;  when  so  expressed  it  is  only  for  the  pur- 
pose of  making  the  subject  clearer  to  the  general  reader. 
The  units  of  weight  or  mass  are  also,  of  necessity,  astro- 
nomical and  not  terrestrial.    The  mass  of  a  body  may  be 
expressed  in  terms  of  that  of  the  sun  or  of  the  earth,  but 
never  in  kilogrammes  or  tons,  unless  in  popular  language. 
There  are  two  reasons  for  this  course.    One  is  that  in  most 
cases  celestial  distances  have  first  to   be  determined  in 
terms  of  some  celestial  unit— the  earth's  distance  from  the 
sun,  for  instance — and  it  is  more  convenient  to  retain  this 
unit  than  to  adopt  a  new  one.     The  other  is  that  the 
values  of  celestial  distances  in  terms  of  ordinary  terrestrial 
units  are  for  the  most  part  uncertain,  while  the  corre- 
sponding values  in  astronomical  units   are  known  with 
great  accuracy. 

An  extreme  instance  of  this  is  afforded  by  the  dimensions 
of  the  solar  system.  By  a  series  of  astronomical  observa- 
tions, investigated  by  means  of  Keplkb's  laws  and  the 
theory  of  gravitation,  it  is  possible  to  determine  the  forms 


forms 

I 


\im 


J  AND  DISTANCE. 

nrSEMXHT. 

yed  by  astronomers 
in  daily  life.    The 
ily  bodies  are  never 
ueosures  for  astro- 
is  only  for  the  pur- 
the  general  reader, 
of  necessity,  astro- 
is  of  a  body  may  be 
)r  of  the  earth,  but 
I  popular  language. 
One  is  that  in  most 
be  determined  in 
's  distance  from  the 
anient  to  retain  this 
B  other  is  that  the 
ordinary  terrestrial 
Q,  while  the  corre- 
B   are  known  with 

id  by  the  dimensions 
tronomical  observa- 
leb's  laws  and  the 
ietermine  the  forms 


MEASUREMENTS  OF  MASS  AND  DISTANCE.      159 

of  the  planetary  orbits,  their  positions,  and  their  dimen- 
sions in  terms  of  the  earth's  mean  distance  from  the  sun 
OS  the  unit  of  measure,  with  great  precision.     Keplek's 
third  law  enables  us  to  determine  the  mean  distance  of  a 
planet  from  the  sun  when  we  know  its  period  of  revolu- 
tion.   All  the  major  planets,  as  far  out  as  Saturn,  have  been 
observed  through  so  many  revolutions  that  their  periodic 
times  can  be  determined  with  great  exactness— in  fact 
within  a  fraction  of  a  millionth  part  of  their  whole  amount. 
The  more  recently  discovered  planets,  Uranus  and  Nep- 
tune, will,  in  the  course  of  time,  have  their  periods  deter- 
mined with  equal  precision.     Then,  if  we  square  the  peri- 
ods expressed  in  years  and  decimals  of  a  year,  and  extract 
the  cube  root  of  this  square,  we  have  the  mean  distance 
of  the  planet  with  the  same  or^cr  of  precision.      This 
distance  is  to  be  corrected  slightly  in  consequence  of  the 
attractions  of  the  planets  on  each  other,  but  these  correc- 
tions also  are  known  with  great  exactness.     Again,  the 
eccentricities  of  the  orbits  are  exactly  determined  by  care- 
ful observations  of  the  positions  of  the  planets  during  suc- 
cessive revolutions.    Thus  we  could  make  a  map  of  the 
planetary  orbits  so  exact  that  the  error  would  entirely 
elude  the  most  careful  scrutiny,  though  the  map  itself 
might  be  many  yards  in  extent. 

On  the  scale  of  this  same  map  we  could  lay  down  the 
magnitudes  of  the  planets  with  as  much  precision  as  our 
instruments  can  measure  their  angular  semidiameters. 
Thus  we  know  that  the  mean  diameter  of  the  sun,  as  seen 
from  the  earth,  is  32';  hence  we  deduce  from  formulse 
already  given  on  pages  5  and  67  that  the  diameter  of  the 
sun  is  .0093083  of  the  distance  of  the  sun  from  the  earth. 
We  oau  therefore,  on  our  supposed  map  of  the  solar  system. 


160 


ABTROhOMT. 


I  < 


!     I 


lay  down  the  sun  in  its  true  size,  according  to  the  scale  of 
the  map,  from  data  given  directly  by  observation.  In  the 
same  way  wo  can  do  tliia  for  each  of  the  planets,  the  earth 
and  moon  excepted.  There  is  no  immediate  and  direct 
way  of  finding  how  large  the  earth  or  moon  would  look 
from  a  planet;  whence  the  exception. 

But  without  further  special  research  into  this  subject, 
we  shall  know  nothing  about  the  scalt  of  our  map.  That 
is,  wo  have  no  means  of  knowing  how  many  miles  or  kilo- 
metres correspond  in  space  to  an  inch  or  a  foot  on  the  map. 
It  is  clear  that  in  order  to  fix  the  distances  or  the  magni- 
tudes of  the  planets  according  to  any  terrestrial  standard, 
we  must  know  this  scale.  Of  course  if  we  can  learn  either 
the  distance  or  magnitude  of  any  one  of  the  planets  laid 
down  on  the  map,  in  miles  or  in  semidiameters  of  the 
earth,  we  shall  be  able  at  once  to  find  the  scale.  But  this 
process  is  so  difficult  that  the  general  custom  of  astrono- 
mers is  not  to  attempt  to  use  a  scale  of  miles,  but  to  employ 
the  mean  distance  of  the  sun  from  the  earth  as  the  unit  in 
celestial  measurements.  Thus,  y^  astronomical  langnage, 
wo  say  that  the  distance  of  Mercury  from  the  sun  is  0.387, 
that  of  Venus  0.7^3,  that  of  Mars  1.523,  that  of  Saturn 
9.539,  and  so  on.  But  this  gives  ns  no  information  respect- 
ing the  distances  and  magnitudes  in  terms  of  terrestrial 
measures.  The  unknown  quantities  of  our  map  are  the 
magnitude  of  the  earth  and  its  distance  from  the  sun  in 
terrestrial  units  of  length.  Could  we  only  take  up  a  point 
of  observation  on  the  sun  or  a  planet,  and  determine  ex- 
actly the  angular  magnitude  of  the  earth  as  seen  from  that 
point,  we  should  be  able  to  lay  down  the  earth  of  oar  map 
in  its  correct  size.  Then,  since  we  already  know  the  size 
of  the  e«rth  in  terrestrial  units  from  geodetic  surteys  we, 


MEASURKMENTa  CV  MASS  AND  DISTANCE.    161 


ng  to  the  scale  of 
ervation.  In  the 
planets,  the  earth 
diate  and  direct 
moon  would  look 

nto  this  subject, 
'  our  map.  That 
any  miles  or  kilo- 
k  foot  on  the  map. 
ces  or  the  magni- 
rrestrial  standard, 
e  can  learn  either 
I  the  planets  laid 
idiametera  of  the 
e  scale.  But  this 
iistom  of  astrono- 
les,  bat  to  employ 
trth  OS  the  unit  in 
lomical  language, 
L  the  sun  is  0.387, 
3,  that  of  Saturn 
formation  respect- 
nns  of  terrestrial 
our  map  are  the 
e  from  the  sun  in 
ly  take  up  a  point 
md  determine  ex- 
as  seen  from  that 
earth  of  our  map 
lady  know  the  size 
Ddetic  surveys  w«, 


should  be  able  to  find  the  scale  of  our  map,  and  thence 
the  dimenfions  of  the  whole  system  in  terms  of  those 
units. 

It  ifill  be  seen  that  what  the  astronomer  really  wants  is 
not  so  much  the  dimensions  of  the  solar  system  in  miles  as 
to  express  the  size  of  the  earth  in  celestial  measures. 
This,  however,  amounts  to  the  same  thing,  because  having 
one,  the  other  can  be  readily  deduced  from  the  known 
magnitude  of  the  earth  in  terrestrial  measures. 

The  magnitude  of  the  earth  is  not  the  only  n  known 
quantity  on  oor  map.  From  Eepleb's  laws  we  can  deter- 
mine nothing  respecting  the  distance  of  the  moon  from  the 
earth,  because  unless  a  change  is  made  in  the  units  of  time 
and  space,  they  apply  only  to  bodies  moving  around  the 
sun.  We  must  therefore  determine  the  distance  of  the 
moon  as  well  as  that  of  the  sun  to  be  able  to  complete  our 
map  on  a  known  scale  of  measurement 

MiAiuxii  or  m  fkiLo  An  ltoax  Paxauax. 

The  problem  of  distances  in  the  solar  system  is  reduced 
by  the  preceding  considerations  to  measuring  the  distances 
of  the  sun  and  moon  in  terms  of  the  earth's  radius.  The 
most  direct  method  of  doing  this  is  by  determining  their 
respective  parallaxes,  which  we  have  shown  to  be  the  same 
as  the  earth's  angular  semidiameter  as  seen  from  them. 
In  the  case  of  the  sun,  the  required  parallax  can  be  deter- 
mined as  readily  by  measuring  the  parallaxes  of  any  of  the 
planets  as  by  measuring  that  of  the  sun,  because  any  one 
measured  distance  on  the  map  will  give  us  the  scale  of  our 
map.  Now,  the  planets  Venus  and  Mars  occasionally 
come  much  nearer  the  earth  than  the  sun  ever  does,  and 
tbeir  parallaxes  also  admit  of  more  exact  measurement 


168 


A8TR0K0MT. 


The  parallax  of  the  sun  ia  therefore  detcrmin*  ,  not  by  ob- 
aenrations  on  the  sun  itself,  but  on  these  two  planets. 

The  general  principles  of  the  method  of  determining  the 
parallax  of  a  planet  by  simultaneous  observations  at  distant 
stations  will  be  seen  by  referring  to  the  figure.  If  two 
observers,  situated  at  S*  and  8",  make  a  simultaneous 
observation  of  the  direction  of  the  body  P,  it  is  evident 
that  the  solution  of  a  plane  triangle  will  give  the  distance 
of  P  from  each  station.     In  practice,  however,  it  would 


Flo.  48. 

be  impracticable  to  make  simultaneous  observations  at 
distant  stations;  and  as  the  planet  is  continually  in  motion, 
the  problem  is  a  much  more  complex  one  than  that  of 
pimply  solving  a  triangle. 

This  is  the  method  of  determining  the  parallax  of  the 
moon.  Knowing  the  actual  figure  of  the  earth,  observa- 
tions of  the  moon  made  at  stations  widely  separated  in 
latitude,  as  Paris  and  the  Cape  of  Good  Hope,  onn  be  com- 
bined so  as  to  give  the  parallax  of  the  moon  and  thni  its 
distance.  On  precisely  the  same  principles  the  parallaxes 
ot  Yww  ox  Mars  have  been  determined. 


iin» !/  not  by  ob- 
ro  planeta. 
letormining  the 
itions  at  distant 
figure.  If  two 
a  flimultaneoai 
P,  it  is  evident 
;ive  the  distance 
iwever,  it  woald 


observations  at 
tually  in  motion, 
le  than  that  of 

)  parallax  of  tho 
e  earth,  obaerVa- 
ely  separated  in 
ope,  onn  be  cbm- 
>on  and  thai  its 
)s  the  parallaxes 


MEASUJiBMEIfTS  OF  MASS  AND  DISTANCE.     163 

Mmt  PftrtUu  frMi  Traaaito  of  ▼•&«••— When  Vtnui  ia  at  ber  in. 
ferior  conjuucliona  ahe  Id  Itetwecu  tliu  iun  and  the  curtli.  If  the 
orbit  of  Vtnu$  lay  in  tlie  ecliptic,  aiiu  would  bo  projected  on  tlie 
auii'a  diilt  at  every  inferior  conjunction.  Tlie  inclination  of  her 
orbit  is,  however,  about  8)°,  and  thus  the  tmntittot  Venu$  occur  only 
when  Venui  happens  to  be  near  the  node  of  her  orbit  at  the  time  of 
inferior  conjunction.  When  this  occurs  she  is  seen  to  pass  ncroaa 
the  sun's  disk.  In  the  last  figure,  if  P  is  the  place  of  Venui  at  such 
a  time,  and  If  Ibe  disk  of  the  sun  is  PP',  then  an  observer  at  8f' 
will  see  V*nu$  at  P'  and  one  at  S'  will  see  her  at  P.  Tho  distance. 
PP'  can  be  meac^rcd  directly,  or  it  can  be  calculated  by  ob^rviug 
th6  time  required  for  V*nu*  to  pass  across  the  chord  of  the  sun's 
disk  at  P'  and  across  the  chord  at  P.  It  is  obvious  that  these 
chords  are  of  different  lengtli. 

The  parallax  of  Venut  («')  is  the  angle  subtended  by  tho  earth's, 
radius  at  P;  the  parallax  of  the  sua  («)  Is  the  angle  subtended  by  the 
earth's  radius  at  P|. 

If  a  Is  the  distance  of  the  earth  from  Vtnu$,  and  If  b  Is  the  distance 
of  the  earth  from  the  sun,  we  know  that  the  earth's  radius  e  will  sub- 
tend an  angle  at  F«nu<  of  -  =  ir*,  and  at  the  sun  of  -^  =  ir  (see  page 


6).     That  U,e  =  tm'  =  iJi  and  «'  =  -.«.     ft  is  leO;  and  a  is 

about  0.26  at  the  time  of  a  transit.    Hence  f^  =  9.8it. 

What  we  really  measure  is  the  difference  of  the  parallaxes  n*  And 
x,  and  thus,  by  employing  the  transit  of  Venus  to  measure  the  sun's  ^ 
parallax  (8".8),  we  are  enabled  to  use  an  angle  2.8  times  as  large,  or 
about  25".  Even  this  Is  •  very  dffHcuU  ihatter:  it  is  hardly  possible 
by  any  one  set  of  measuros-of  the  solar  parallax  to  determine  the  latter 
without  an  uncertainty  of  ^^  of  iu  whole  amount.  In  the  distance 
of  the  ittn  this  corresponds  to  an  uncertainty  of  nearly  half  a  million 
of  miles.  Astronomers  have  therefore  sought  for  other  methods  of 
determi|iiog  the  sun's  distance.  Although  some  of  these  may  be 
a  little  more  certain  than  measures  of.  parallax,  there  Is  none  by 
which  the  distance  of  the  sun  itf  miles  can  be  determined  with  any 
approximation  to  the  accuracy  which  characterizes  otber  celestial 
meiwures. 

'Othtr  MMHodi  of  Determining  Solar  Purillax.— A  very 
interesting  and  probably  the  most  accurate  method  of 
meaduring  the  sun's  distance  depends  upon  a  knowledge  of 
the  Telocity  of  light.    We  shall  hereafter  see  that  the  time 


164 


ASTRONOMY. 


required  for  light  to  pass  from  the  son  to  the  earth  is  known 
with  considerable  exactness,  being  very  nearly  498  seconds. 
This  time  can  be  determined  still  more  aecuratefy.    K 
then  we  can  determine  experimentally  how  many  miles  or 
kilometres  light  moves  in  a  second,  we  shall  at  once  have 
the  distance  of  the  sun  by  multiplying  that  quantity  by 
498.    The  velocity  of  lig^t  is  about  300,000  kilometres 
per  second.    This  distance  would  reach  about  eight  times 
around  the  ewth.    It  is  seldom  poasible  to  see  two  points 
on  the  earth's  surface  more  than  n  hundred  kilometree 
apart,  and  distinct  vision  sjt  distances  of  more  than  tweaty 
kilometres  is  rare.    Hence  io  determine  experimentally  ttic 
time  required  for  light  to  pass  between  two  terrestrial  sta- 
tions requires  the  measurement  of  an  interval  of  time 
which,  even  under  the  most  favorable  cases^  can  be  only  a 
fraction  of  a  thousandth  of  a  second.    Methf)ds  of  doing 
it,  however,  have  been  devise#,  and  the  vel  jcity  of  Kghfr 
would  seem  to  be  about  299,900  kilometres  per  8eeond>. 
Multiplying  this  by  498,  we  obtain  149,350,000  kilometres 
(a  little  less  than  93,000,000  miles)  for  the  disfamee  of  the 
SUB.    The  time  required  for  light  to  pass  horn  the  sun  to 
the  earth  is  still  uncertain  by  nearly  a  second,  but  l&is 
value  of  the  sun's  distance  is  probably  tiie  best  yet  ob- 
tained.   The  corresponding^  vmlue  of  the-  sun's  panBiC  is 
8'.81. 

Yet  other  methods  of  detemin^ng  the  sun's  dirtaBov 
are  given  by  the  theory  of  gra<4t«tion.  It  is  found  hf 
mathematical  investigation  that  the  motion  of  the  moon  is 
subject  to  several  inequalities,  hnving  the  sim's  horiwnilil 
parallax  as  a  factor^  If  the  position  of  the  moon  owdt  Hv 
determined  by  observation  with  the  same  easotOMK  tMr 
j)he  ponHoa^  » 9^  v/^  nlwiet  c»n  (whidl  il^ewwi^lKD^ 


IjIa 


earth  is  known 
ly  498  seconds, 
uocuratefy.  If 
many  miles  or 
[I  at  once  have 
at  quantity  by 

000  kilometres 
ut  eight  times 

see  two  points 
red  kilometree 
ire  than  twenty 
erimentally  Idic 

terrestrial  sta- 
terval  of  lime 
1^  can  be  only  a 
!thr>dB  of  doing 
el  jcity  of  Kght 
«8  per  seeontf. 
1,000  kilometres 
distanee  of  the 
^m'  the  sBtt  to' 
econd,  bat  l&is 
Im  best  yet  ob* 
Hin's  panBaK  is 

Ban's  dirtaBov 
It  is  fottod  fijr 
t  of  the  moon  ia 
Hut's  horiMartri 

1  moon  oaoit  Hv 


^i«<«HH*«iH 


MEASUREMENTS  OF  MASS  AND  DISTANCE.     166 

this  would  probably  afford  the  most  accurate  method  of 
determining  the  solar  parallax. 

Brief  Hlitory  of  Detarmiiiatioiu  of  the  SoUr  PutlUz.— The  dctermi- 
natioa  of  the  distance  of  tlie  sun  must  at  all  times  have  been  one  of 
the  most  interesting  scientific  problems  presented  to  the  human  mind. 
The  first  known  attempt  to  effect  &  solution  of  the  problem  was  made 
by  Aristarchus,  who  flourished  in  the  third  century  before  Christ. 
It  was  founded  on  the  principle  that  the  time  of  the  moon's  first 
quarter  will  vary  with  the  ratio  between  the  distance  of  the  moon 
and  Sim,  which  may  be  shown  as  follows.  In  Fig.  50  let  E  represent 
the  earth,  M  the  moon,  and  S  the  sun.  Since  the  sun  always 
illuminates  one  lialf  of  the  lunar  globe,  it  is  evident  tliat  when  one 


rtekflOL 

half  of  the  moon's  disk  appears  illuminated  the  triangle  ^  JT^muat 
be  right-angled  at  M.  The  angle  MBS  can  be  determined  by 
measurement,  being  equal  to  the  angular  distance  between  the  sun 
and  the  moon.  Having  two  of  tiie  angles,  the  third  can  be  deter- 
mined, because  the  sum  of  the  three  must  make  two  right  angles. 
Thence  we  shall  have  the  ratio  between  E  M,  the  distance  of  the  moon, 
and  E8,  tlie  diatance  of  the  sun.  by  a  trigonometrical  computation. 
Then  knowing  the  distance  of  the  moon,  which  can  be  determined 
with  comparative  ease  (see  page  182),  we  have  the  distance  of  the  sun 
by  multiplying  by  this  ratio.  Aristabchcs  concluded,  from  his 
suppoied  measures,  tliat  the  r.ngle  MBS  waa  three  degrees  less  than 

EM       1 
a  right  angle.    We  aliould  then  have  ^^-  =  rrr  vr^  nearly,  since  8* 

ia  ^  of  57*  and  B8  =  57°  (sec  page  6).  It  would  follow  from  tiiis 
tluit  tli»  tm  wM  19  timea  the  diatancQ  ot  it»  moon.    We  now  know 


166 


A8TB0N0MT. 


that  this  result  is  entirely  wrong,  and  that  it  is  so  because  it  is  im- 
possible to  determine  the  time  when  the  moon  is  exactly  half  illumi- 
nated with  any  approach  to  the  accuracy  necessary  in  the  solution  of 
the  problem.  In  fact,  the  greatest  angular  distance  of  the  earth  and 
moon,  as  seen  from  the  suu — that  is,  the  angle  ESM— is  only  about 
one  quarter  the  angular  diameter  of  the  moon  as  seen  from  the 
earth. 

The  second  attempt  to  determine  the  distance  of  the  sun  is  men- 
tioned by  Ptoleht,  though  Hippakchus  may  be  the  real  inventor 
of  it.  It  is  founded  on  a  somewhat  complex  geometrical  construc- 
tion of  a  total  eclipse  of  the  moon.  It  is  only  necessary  to  state  the 
result,  which  was  that  the  sun  was  situated  at  the  distance  of  1210 
radii  of  the  earth.  This  result,  like  the  former,  was  due  only  to 
errors  of  observation.  So  far  as  all  the  methods  known  at  the  time 
could  show,  the  real  distance  of  the  sun  appeared  to  be  infinite; 
nevertheless  ProiiBMY's  result  was  received  without  question  for 
fourteen  centuries. 

Th3  first  really  successful  measure  of  the  parallax  of  a  planet  was 
made  upon  Mar$  during  the  opposition  of  1672,  by  the  first  of  the 
two  methods  already  described.  An  expedition  was  sent  to  the 
colony  of  Cayenne  to  observe  the  declination  of  the  planet  from 
night  to  night,  while  corresponding  observations  were  made  at  the 
Paris.  Observatory.  From  a  discussion  of  these  observations.  Cab- 
siNi  obtained  a  solar  pandlax  of  9". 5,  which  is  within  a  second  of 
the  truth.  The  next  steps  forward  were  made  by  the  transits  of 
Venua  in  1761  and  1769.  The  Itsading  civilized  nations  caused  obser- 
vations on  tliese  transits  to  be  made  at  various  points  on  the  globe. 
The  method  used  was  vsry  simple,  consisting  in  the  determination 
of  the  times  at  which  Venu*  entered  upon  the  sun's  disk  and  left  it 
•gain.  The  absolute  times  of  ingress  and  egress,  as  seen  from  differ- 
ent points  of  the  globe,  might  differ  by  20  minutes  or  more  on  ac- 
count of  parallax.  Tlie  results,  however,  were  found  to  be  discord- 
ant. It  was  not  until  more  than  half  a  century  had  elapsed  that  the 
observations  were  systematically  calculated  by  Enckb  of  Qermany, 
who  concluded  that  the  parallax  of  the  sun  was  8"  .578,  and  the  dis- 
tance 95  millions  of  miles. 

In  1854  it  began  to  be  suspected  that  Enokb's  value  of  the  parallax 
was  much  too  small.  Hansen,  from  the  theory  of  the  moon,  found 
the  parallax  of  the  sun  to  be  S"  .916.  This  result  seemed  to  be  con- 
firmed by  other  observations,  especially  those  of  Man  during  1868. 
It  was  therefore  concluded  that  the  sun's  parallax  was  probably  be- 
tween 8"  .90  and  9"  .00.  Subsequent  researches  have,  however,  been 
diminishing  thia  Ttlue.    In  1867,  from  a  discustioa  of  itll  Ui«t  data 


MBASUREMUNfS  Of  MAB8  AND  DISTANCE.     167 


lecause  it  is  im- 
jtly  half  illumi- 
1  the  solution  of 
of  the  earth  and 
r— is  only  about 
seen  from  the 

the  van  is  meu- 
le  real  inventor 
Eitrieal  construc- 
isury  to  state  the 
listanee  of  1210 
iras  due  only  to 
lown  at  the  time 
d  to  be  infinite; 
>ut  question  for 

:  of  a  planet  was 
'  the  first  of  tlie 
was  sent  to  tlie 
the  planet  from 
ere  made  at  the 
bservatious,  Gas- 
hin  a  second  of 
y  the  transits  of 
ons  ca\ised  obser- 
its  on  the  globe, 
be  determination 
s  disk  and  left  it 
seen  from  differ- 
i  or  more  on  ac- 
nd  to  be  discord- 
1  elapsed  that  the 
:ke  of  Germany, 
.578.  and  the  dis- 

ue  of  the  parallax 
'  the  moon,  found 
seemed  to  be  con- 
Van  during  1868. 
was  probably  bc- 
^ve,  howeTef.  been 
o  of  W  tl>«t  d»ta 


which  were  considered  of  value,  it  was  concluded  by  one  of  the 
writers  that  the  most  probable  parallax  was  8". 848.  The  measures 
of  the  velocity  of  light  reduce  this  value  to  8". 81,  and  it  is  now 
doubtful  whether  the  true  value  is  any  larger  than  this. 

All  we  can  say  at  present  is  that  the  solar  parallax  is  probably  be- 
tween 8". 79  and  8". 83,  or,  if  ouUide  these  limits,  that  it  can  be  very 
little  outside. 

Relative  Masses  or  the  Suh  and  Flakets. 

In  estimating  celestial  masses  as  well  as  distances,  it  is  necessary 
to  use  what  we  may  call  celestial  units;  ihiit  is,  to  take  Uie  mass  of 
some  celestial  b>xly  as  a  unit,  instead  of  nny  multiple  of  the  pound  or 
kilogram.  Tlie  reason  of  this  is  that  the  rntiu»  between  the  musses 
of  the  planetary  system,  or,  which  is  the  same  thirtg,  tlie  mass  of 
e.ich  body  in  terms  of  that  of  some  one  body  ns  the  unit,  can  be;  de- 
tcrmiped  independently  of  the  mass  of  nny  one  of  them.  To  express 
a  mass  in  kilogrammes  or  other  terrestrial  units,  it  is  necessary  to  find 
the  mass  of  the  earth  in  such  units,  as  already  explained.  This, 
however,  is  not  necessary  for  astronomical  purposes,  where  only  the 
relative  masses  of  the  several  planets  are  required.  In  estimating 
the  masses  of  the  individual  planets,  that  of  the  sun  is  generally 
taken  as  a  unit.  The  planetary  masses  will  then  all  be  very  small 
fractions. 

The  mass  of  the  sun  being  1.00,  the  mass  of  Mercury  is  ^Jcti; 

"  "  Venu»      is  tT^m\ 

"  '•  "  "         JEa>'</*     is  rnVw: 

Man       is„^,T»; 
"  "  "  "  "         Jupiter    isj^; 

"  "  "  "  "         Saturn    isjAxS 

"  '<  ••  "  '  Uraniu  is  niwl 

"  •'  "  "  "         Neptu,'     rtiiif 

MtMM  of  tlw  Xurfh  and  Son.— The  mau  of  the  esria  :n  <:3Dnected 
by  a  very  curious  relation  with  the  paralla.t  of  '>«  sun.  Knowing 
the  latter,  we  can  determine  the  mass  of  the  suu  rvlstivo  o  tbr  earlii, 
which  is  the  same  thing  as  determining  the  astronor^r '"^)  niisi  of  the 
earth,  that  of  the  sun  being  unity.  This  mny  be  cle:triy  seen  by  re- 
flecting that  when  we  know  the  radius  of  the  eariL's  orbit  we  rnn 
determine  how  far  the  earth  moves  aside  froo*  .>  .might  line  in  oua 
second  in  consequence  of  the  attraction  of  tho  lui;.  This  muticn 
measures  the  attractive  force  of  the  sun  at  the  distance  of  the  eutb 


IttJBlW.Mgag'i.iW 


168 


A8TR0N0MT. 


Compnring  it  with  the  attractive  force  of  the  earth,  and  making 
allowance  for  the  difference  of  distunccs  from  centres  of  the  two 
boilics,  we  determine  the  ratio  between  their  masses. 

Tlie  following  table  shows,  for  different  values  of  the  solar  paral- 
lax, the  corresponding  ratio  of  the  masses,  and  distance  of  the  sun  in 
terrestrial  measures: 


DiaTAMCB  or  trk  Sl'M 

Solar 

M 

Parallax. 

P" 

In  eqMRtorial 

radu  of  the 

earth. 

In  mllUona  of 
miles. 

In  millions  of 
kilometres. 

8'.  77 

835684 

23519 

93.208 

150.001 

8".  78 

834598 

28492 

98.102 

149.830 

8'.  79 

383398 

28466 

92.996 

149.660 

8". 80 

832262 

23439 

92.890 

148.490 

8".  81 

331182 

23413 

92.785 

149.320 

8'.  82 

330007 

23386 

92.680 

149.161 

8". 88 

338887 

23360 

92.575 

148.982 

We  have  said  that  the  solar  parallax  is  probably  contained  Iwtween 
the  limits  8". 79  and  8". 88.  It  is  certainly  hardly  more  than  one  or 
two  hundredtlis  of  a  second  without  them.  So,  if  we  wish  to  ex- 
press the  constants  relating  to  the  sun  in  round  numbers,  we  may 
say  that — 

Its  matt  is  830,000  times  that  of  the  earth. 

Its  dMtanee  in  miles  is  93  millions,  or  perhaps  a  little  less. 

lU  distance  in  kilometres  is  probably  between  149  and  150  mil- 
lions. 


til,  and  making 
tres  of  tbe  two 

the  solur  parol- 
ice  of  the  Bun  in 


Sum 


In  millions  of 
kilometres. 


150.001 
149.890 
149.6tf0 
148.490 
149.320 
149. ISl 
148.983 


ntained  Itetween 

ore  than  one  or 

we  wish  to  ex- 

imbcrs,  we  may 


tie  less. 

19  aud  160  mil- 


CHAPTER  XL 

TKE  BEPBACTION  AND  ABERRATION  OP  LIGHT  AND 

TWILIGHT. 

Aivofranio  BBnAcmar. 

Wnsv  we  qieak  of  the  place  of  a  planet  or  star,  we  n«a- 
ally  mean  its  true  place;  i.e.,  its  direction  from  an  ob- 
server situated  at  the  centre  of  tbe  eartb.  We  have  tbowi 
in  the  section  on  parallax  how  observations  which  are 
.necessarily  taken  at  tbe  surface  off  the  earth  are  reduced 
to  what  they  would  have  been  if  the  observer  were  situated 
at  the  earth's  centre.  We  have  supposed  tbe  star  to  be 
projected  on  the  celestial  sphere  in  the  prolongation  of 
the  line  joining  the  observer  and  the  star.  The  ray  from 
the  atw  was  considered  to  si^er  no  deflection  in  passing 
throng  the  stellar  spaces  and  through  the  earth's  atmos- 
phww.  Bat  from  the  principles  of  physics,  we  know  that 
Booh  a  InminouB  ray  passing  from  an  empty  space  (as  the 
fltellM-  Bpaoei  prehirt^  are),  and  through  an  aitmosphere, 
matt  Boiier  •  refeactioo,  as  every  ray  of  light  is  known  to 
do  ni  -pMirinf  from  a  tam  into  a  denser  medittm.  As  we 
MB^tite  stw  in  tito  diteetion  in  which  its  light  enters  ihe 
rnyo  Hint  is,  m  wo  {urojeet  the  star  on  the  celestial  sphere 
byiprokm^iog  this  light-bewn  backward  into  space— there 
9-i:'!:  Mm^tfpfmuAiiiukjitMmttata  the  star  Irom  refrac- 
twa. 

W«  mtjj  recall  »  tew  deflnitions  from  physics.    The  ray  which 
toavM  tbe  Mar  and  imj^tiges  on  the  outer  surface  of  tbe  «arth'a  at- 


ABTRONOMT. 


^mgi 


mospbcre  is  called  the  incident  ray;  after  its  deflection  by  the  attnos* 
phere  it  in  called  the  refracted  ray.  The  difference  between  these 
diiections  is  called  the  aetronomieal  refraction.  If  a  normal  is  drawn 
(perpendicular)  to  the  surface  of  the  refracting  medium  at  the  point 
where  the  incident  ray  meets  it,  the  acute  angle  between  the  incident 
ray  and  the  normal  is  callM  the  angle  of  incidence,  and  the  acute  angle 

between  the  normal  and  the  refracted 
ray  is  called  the  angle  of  refraction. 
The  refraction  itself  is  the  difference 
of  these  angles.  The  normal  and 
both  incident  and  refracted  rays  are 
in  tlie  same  vertical  plane.  In  Fig. 
51,  SA  is  the  ray  incident  upon  the 
surface  ^.^  of  the  refracting  medium 
BBAN,  AO  is  the  refracted  ray, 
MNWxo  normali  ,8^  Jf  and  CAN 
the  angles  nt  incideuco  and  refrac- 
tion respectively.  Produce  CA  back- 
ward iij  the  direction  A  ff:  8 A  S  is 
the  refraction.  An  observer  at  G  will 
see  the  star  8  as  if  it  were  at  S.  AS  is  the  apparent  direction  of 
the  ray  coming  from  the  star  8,  and  8  is  the  apparent  place  of  the  star 
as  affected  by  refraction. 


St.— Refiuctioii. 


This  explanation  supposes  the  space  above  BB'  in  the 
figure  to  be  entirely  empty,  and  the  earth's  atmospherei, 
equally  dense  throughout,  to  fill  the  space  below. .&i?'. 
In  fact,  however,  the  earth's  atmosphere  is  most  dense 
dt  the  surface  of  the  earthj  and  gradually  diminishes  in 
density  to  its  exterior  boundary.  .  Therefore  we  must  sup- 
pose the. atmosphere  to  be  divided  into  a  great  number  of 
parallel  layers  of  air,  and  by  assuming  an  infinite  nnmr 
her  of  these  we  may  also  assume  that  throughout  each  one 
of  them  the  air  is  equally  dense.  Hence  the  preoediog 
figure  will  only  represent  the  refraction  at  a  single  one  of 
these  layers.  The  path  of  a  ray  of  light  through  the  at* 
mosphere  is  not  a  straight  line  like  A  C,  but  a  curve,  l^^e 
may  suppose  this  curve  to  be  represented  in  Fig.  02,  where 


>n  by  the  attno»> 
e  between  these 
normal  is  drawn 
im  at  the  point 
een  the  incident 

the  acute  angle 
nd  the  refracted 
le  of  refraction. 
is  the  difference 
le  normal  and 
^racted  rays  are 
plane.  In  Fig. 
idcut  upon  tlio 
racting  medium 

refracted  ray. 
IJf  and  CAN 
Qco  and  refrac- 
aduce  CA  baclc- 
I  Aff.'SAB  ia 
laerver  at  G  will 
!ut  direction  o| 
]^aee  of  the  star 


e  BB'  in  the 
3  atmosphere^ 

below. -ffi?', 
I  most  dense 
diminishes  in 
we  must  Bup- 
»t  nnmber  of 
infinite  namr 
loat  each  one 
the  preoediQg 

single  one  of 
iroogh  the  at? 
a  curre.  Ve 
rig.  02,  where 


HEFRACTION  AND  ABERRATION  OF  LIGHT,     m 

the  number  of  layers  has  been  taken  very  small  to  avoid 
confusing  tho  drawing. 

Lot  C  be  tho  centre  and  A  a  point  of  the  surface  of  the 
earth;  let  Shoa  star,  and  >S^e  a  ruy  from  the  star  which  is 
refracted  at  the  varioiis  layers  into  which  we  suppose  the 
atmosphere  to  be  divided,  and  which  finali '  enters  tho  eye 
of  an  observer  at  ^  in  tho  apparent  di.oction  S'A.    He 


Vm.  as.— BKFRAonoR  or  Lathh  or  Alfe. 

will  then  see  the  star  in  the  direction  S*  instead  of  that  of 
^S",  and  ■'J AS',  the  refraction,  will  throw  the  star  nearer 
to  his  zenith  Z. 

The  angle  8' A  Z 19  the  apparent  zenith  distance  ot  S; 
t^e.true  zenith  distance  of  S  is  ZA  iS,  and  SA  may  be 
assumed  to  coincide  with  iS^0,  as  for  all  heavenly  bodies 
except  the  moon  it  pra<;tioally  does.    The  line  Se  pro- 


ABTR0N0M7. 


longed  will  meet  the  line  AZ'\n%  point  above  A,  eoppoie 
at  v. 

Quantity  and  Effeeti  of  Xefraotion. — At  the  zenith  the 
refraction  is  0,  at  45°  zenith  distance  the  refraction  is  about 
l^  and  at  90°  it  is  34'  30";  that  is,  bodies  at  the  zenith 
distances  of  45°  and  90°  appear  elevated  above  their  tme 
places  by  V  and  34^'  respectively.  If  the  snn  has  just 
risen — that  is,  if  its  lower  limb  is  just  in  apparent  contact 
with  the  horizon — it  is  in  fact  entirely  below  the  true 
horizon,  for  the  refraction  (35')  has  elevated  its  centre  by 
more  tlian  its  whole  apparent  diameter  (32'). 

The  moon  is  full  when  it  is  exactly  opposite  the  sun, 
and  therefore,  were  there  uo  atmosphere,  moon-rise  of  a 
full  moon  and  sunset  would  be  simultaneous.  In  fact, 
both  bodies  being  elevated  by  refraction,  we  see  the  full 
moon  risen  before  the  sun  has  set.  On  April  20th,  1837, 
the  full  moon  rose  eclipsed  before  the  (ran  had  set. 

TWIUOHT. 

It  is  plain  that  one  effect  of  refraction  is  to  lengthen  the 
duration  of  daylight  by  causing  the  snn  to  appear  above 
the  horizon  before  the  time  d!  his  geomeirieal  rising  and 
after  the  time  of  true  sunset.    . 

Daylight  is  also  prolonged  by  the  reflection  of  the  sun's 
rays  (after  snnset  and  before  sanrise)  from  the  small  parti- 
cles of  matter  suspended  in  the  atmosphere.  This  i»o- 
duces  a  general  though  faint  illumination  of  the  atmos- 
phere, just  as  the  light  scattered  from  the  floating  particles 
of  dnst  illuminated  by  a  sunbeam  let  in  through  a  titmSk 
in  a  shntter  may  brighten  the  whole  of  a  darkened  room. 

The  sun's  direct  rays  do  not  reach  an  <rtieerver  on  tiie 


K>Te  A,  BUppOM 

the  zenith  the 
raotion  is  about 
s  at  the  zenith 
bovo  their  tnie 
e  Ban  has  just 
pparent  contact 
below  the  true 
)d  its  centre  by 

posite  the  sun, 
moon-rise  of  a 
eouB.  Ic  fact, 
ire  see  the  full 
iril  20th,  1837, 
tad  set. 


to  lengthen  the 
4)  appear  above 
ieal  rising  and 

ion  of  the  sun's 
the  BDudl  p«rti- 
ere.  This  iffo- 
of  the  stmoB- 
ioating  particles 
brongh  a  €iadc 
urkened  reoin. 
Ametfer  on  tiie 


TWIUOST. 


178 


earth  after  the  instant  of  sunset,  since  the  solid  body  of 
the  earth  intercepts  them.  But  the  sun's  direct  rays 
illuminate  the  clouds  and  the  suspended  particles  of  the 
upper  air,  and  are  reflected  downwards  so  as  to  produce  a 
general  illumination  of  the  atmosphere. 

In  the  figure  let  -4  ^  CZ>  be  the  earth  and  A  an  observer 
on  its  surface,  to  whom  the  sun  S  is  just  setting.  ^  a  is 
the  horizon  of  A;  Bbot  B;  Cc  of  C;  Dd  otD.    Let  the 


no.  Bs. 


circle  PQR  represent  the  upper  layer  of  the  atmosphere. 
Between  ABGD  and  PQR  the  air  is  filled  with  sus- 
pended particles  which  will  reflect  light.  The  lowest  ray 
of  the  Bun,  SAM,  just  grazes  the  earth  at  A  ;  the  higher 
rays  iS^iVand  SO  strike  the  atmosphere  above  A  and  leave 
it  at  the  points  Q  and  B.  Each  of  the  lines  SAPM, 
SQN,  is  bent  from  a  straight  course  by  refraction,  bat 
SB  0  is  not  bent  since  it  just  touches  the  upper  limit*  of 


ASTRONOilV. 


n 


lii 


ft*;. 


Ji 


the  atmosphere.  The  space  MA  li  C DB  ia  the  earth's 
shadow.  An  observer  at  A  receives  the  (last)  direct  rays 
from  the  sun,  and  also  has  his  sky  illuminited  by  the  reflec- 
tion from  all  the  particles  lying  in  the  space  PQJiT 
which  is  all  above  his  horizon  A  a. 

An  observer  at  B  receives  no  direct  rays  from  the  sun. 
It  is  after  sunset.  Nor  does  he  receive  any  light  from  all 
that  portion  of  the  atmosphere  below  A  /'  M;  but,the  por- 
tion PRx,  which  lies  above  his  horizon  U  b,  is  lighted  by 
the  sun's  rays,  and  rofloets  to  B  a  portion  of  the  incident 
rays. 

This  ttoilight  is  strongest  at  R,  and  fades  away  gradu- 
ally toward  P. 

To  an  observer  at  C  the  twilight  is  derivoJ  from  the 
illumination  of  the  portion  PQz  which  lies  above  his 
horizon  Cc.  ^ 

To  an  observer  at  Z>  it  is  night.  All  ol  the  illt^mated 
atmosphere  is  below  his  horizon />rf. 

The  student  should  notice  for  himself  the  twilight  arch 
which  appears  in  the  west  after  sunset.  It  is  morti  marked 
in  summer  than  in  winter;  in  high  latitudes  than  in  low 
ones.  There  is  no  true  night  in  England  in  midsiiinmer, 
for  example,  the  morning  twilight  beginning  before  the 
evening  twilight  has  ended ;  and  in  the  torrid  zone  there 
is  no  perceptible  twilight. 

Abebbatioh  ahd  the  Motioh  of  Liokt.  , 

Besides  refi-action,  there  is  another  cause  which  prevents 
our  seeing  the  celestial  bodies  exactly  in  the  true  direction 
in  which  they  lie  from  us;  namely,  the  progressive  mo- 
tion of  light.  We  see  objects  only  by  the  light  which 
emanates  from  them  and  reaches  our  eyes,  and  we  know 


F  is  the  earth's 

lust)  direct  rays 

ted  by  the  reflec- 

space  PQRT 

B  from  the  sun. 
y  light  from  all 
M;  but^the  por- 
i  b,  is  lighted  by 
of  the  incident 

des  away  gradu- 

erivoJ  from  the 
lies   above    his 

the  illi^mated 

th0  twiUght  arch 
t  is  mote  marked 
des  than  in  low 
in  midsummer, 
ining  before  the 
torrid  zone  there 


F  LlOKT.  , 

le  which  prevents 

the  true  direction 

progressive  mo- 

the  light  which 

es,  and  we  know 


REFRACTION  AND  ABERRATION  OF  LIGHT.     175 

that  this  light  requires  time  to  pass  over  the  space  which 
separates  us  from  the  luminous  object.  After  the  ray  of 
liglit  once  leaves  the  object,  the  latter  may  move  awaiy,  or 
even  be  blotted  out  of  existence,  but  the  ray  of  liglit 
will  continue  on  its  course.  Consequently  when  we  look 
at  a  star,  we  do  not  see  the  star  that  now  is,  but  the  star 
that  was  several  years  ago.  If  it  should  be  annihilated,  we 
should  still  see  it  during  the  years  which  would  be  required 
for  the  last  ray  of  light  emitted  by  it  to  reach  us.  The 
velocity  of  light  is  so  great  that  in  all  observations  of  ter- 
restrial objects  our  vision  may  be  regar<l  '1  as  instantane- 
ous. But  in  celestial  observations  the  u\  '^quired  for 
the  light  to  reach  us  is  quite  appreciable  and  arable. 

The  discovery  of  the  propagation  of  liglu       among  the 
most  remarkable  of  those  made  by  modern  science.     The 
fact  tliat  light  requires  time  to  travel  was  first  learned  by 
the  observations  of  the  satellites  of  Jupiter.    Owing  to 
the  great  magnitude  of  this  planet,  it  casts  a  much  longer 
and  larger  shadow  than  our  earth  does,  and  its  inner  sat- 
ellite passes  through  this  shadow  and  is  eclipsed,  at  every 
revolution.    These  ecliiJses  can  be  observed  from  the  earth, 
the  satellite  vanishing  from  view  as  it  enters  the  shadow, 
and  reappearing  when  it  leaves  it  again.    The  astronomers 
of  tlie  seventeenth  century  made  a  careful  study  of  the  mo- 
tions of  these  bodies.     It  was,  however,  necessary  to  con- 
struct tables  by  which  the  times  of  the  eclipses  could  le  pre- 
dicted.   It  was  found  by  Roemer  that  these  times  depended 
on  the  distance  of  Jupiter  from  the  earth.    If  he  made  his 
tables  agree  with  observations  when  the  earth  was  nearest 
Jupiter,  it  was  found  that  as  the  earth  receded  from  Jupiter 
in  its  annual  course  around  the  sun,  the  eclipses  were  con- 
stantly seen  later,  until,  when  at  its  greatest  distance,  the 


W" 


176 


AaTROKOMT. 


times  appeared  to  be  22  minntca  late.  Roexbr  saw  that  it 
was  in  the  highest  degree  improbublo  that  tlic  actual  motions 
of  the  satellites  should  be  atFectcd  witii  any  such  inequality; 
he  therefore  propounded  the  bold  tlieory  that  it  took  time 
for  light  to  come  from  Jupiter  to  the  oiirth.  The  extreme 
differences  in  the  times  of  the  eclipse  being  22  minutes,  he 
assigned  this  as  the  time  required  for  light  to  cross  the 
orbit  of  the  earth,  and  so  concluded  that  it  came  from  the 
sun  to  the  earth  in  11  minutes.  This  estimate  was  too 
great;  the  true  time  for  this  passage  being  about  8  minutes 
and  18  seconds. 

DiieoTtry  of  Aberration. — This  theory  of  Robmbb  was 
not  fully  accepted  by  his  contemporaries.  But  in  the  year 
1729  the  celebrated  Bradlbt,  afterward  Astronomer  Royal 
of  England,  discovered  a  ph'>nomenon  of  an  entirely  dif- 
ferent character,  which  coiifii-mcd  the  theory.  He  was 
then  engaged  in  making  observations  on  the  star  y  Dra- 
conia  in  order  to  determine  its  parallax.  The  effect  of 
parallax  would  have  been  to  make  the  declination  of  the 
star  greatest  in  June  and  least  in  December,  while  in 
March  and  September  the  star  would  occupy  an  interme- 
diate or  r  e^rn  p  i<tion.  Bnt  the  result  was  entirely  dif- 
ferent. Ir  ■  dec  iAtions  of  Jane  and  December  were  the 
same,  shocking  no  effect  of  parallax;  but  instead  of  remain- 
ing c  .  Unt  the  rest  of  the  year,  the  declination  was  some 
40  seconds  greater  in  September  than  in  March,  when  the 
effect  of  parallax  would  be  the  same.  This  showed  that 
the  direction  of  the  star  appeared  different,  not  according 
to  the  position  of  the  earth  in  its  orbit,  but  according  to 
the  direction  of  the  earth's  motion  around  the  sun,  the 
star  being  apparently  displaced  in  this  direction. 

To  9how  bow  this  is,  let  AB  h^  th?  optical  axis  of  « 


MER  saw  that  it 
0  actnul  motions 
such  inequality; 
Itut  it  took  time 
.  Tho  extreme 
22  minutes,  he 
[ht  to  cross  the 
:  came  from  the 
Btimiite  was  too 
about  8  minutes 

of  RoBMBB  was 
But  in  the  year 
itronomer  Royal 
an  entirely  dif- 
lieory.     He  was 
the  star  y  Dra- 
The  effect  of 
olination  of  the 
jmber,  while  in 
npy  an  interme- 
Kras  entirely  dif- 
cember  were  the 
latead  of  remain- 
nation  was  some 
if  arch,  when  the 
his  showed  that 
it,  not  according 
but  according  to 
tnd  the  sun,  the 
ection. 
>ptical  axis  of  a 


"WSS-^ 


■^  -wrrw^iwif  fs^r^-- 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0 


1.1 


if  EM  1^ 

£   lit   12.0 

lit 


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Ife. 


REFRACTION  AND  ABERRATION  OF  LIGHT.     177 


_ 


telescope,  and  8  a  star  from  which  emanates  a  ray  moving 
in  the  true  direction  SAB'.  Per- 
haps the  student  will  have  a  clearer 
conception  of  the  subject  if  he  imag- 
ines AP  to  be  a  rod  which  an  ob- 
server at  B  seeks  to  point  at  the  star 
S.  It  is  evident  that  he  will  point 
this  rod  in  such  a  way  that  the  ray 
of  light  shall  run  accurately  along  its 
length.  Suppose  now  that  the  ob- 
serrer  is  moving  from  B  toward  B' 
with  such  a  velocity  that  he  moves  J^"-  H 

from  B  to  B'  during  the  time  required  for  a  ray  of  light  to 
move  fi?om  A  to  B'.  Suppose,  also,  that  the  ray  of  light 
8A  reaches  A  at  the  same  time  that  the  end  of  his  rod 
does.  Then  it  is  clear  that  while  the  rod  is  moving  from 
the  position  AB  to  the  position  A'B',  the  ray  of  light 
will  move  from  A  to  B',  and  will  therefore  run  accurately 
along  the  length  of  the  rod.  For  instance,  if  b  is  one  third 
of  the  way  from  B  to  B',  then  the  light,  at  the  instant  of 
the  rod  takirig  the  position  i  a,  will  be  one  third  of  the  way 
from  A  to  B',  and  will  therefore  be  accurately  on  the  rod. 
Consequently,  to  the  observer,  the  rod  will  appear  to  be 
pointed  at  the  star.  In  reality,  however,  the  pointing  will 
not  be  in  the  true  direction  of  the  star,  but  will  deviate 
from  it  by  a  certain  angle  depending  upon  the  ratio  of  the 
velocity  with  which  the  observer  is  carried  along  to  the 
velocity  of  light  This  presupposes  f  ;iat  the  motion  of  the 
observer  is  at  right  angles  to  that  of  a  ray  of  light.  If 
this  is  not  his  direction,  we  must  resolve  his  velocity  into 
two  components,  one  at  right  angles  to  the  ray  and  one 
pAfiaW  to  it.    The  latter  will  not  a^e^t  jibe  apparent  di- 


178 


ASTRONOMY. 


rection  of  the  star,  which  will  therefore  depend  entirely 
upon  the  former. 

Effeott  of  Aberration.— The  apparent  displacement  of 
the  heavenly  bodies  thus  produced  is  called  the  aberration 
of  light.  Its  effect  is  to  cause  each  of  the  fixed  stars  to 
ascribe  an  apparent  annual  oscillation  in  a  very  small  orbit. 
The  nature  of  the  displacement  may  be  conceived  of  in  thfe 
following  way:  Suppose  the  earth  at  any  moment,  in  the 
course  of  its  annual  revolution,  to  be  moving  toward  a 
point  of  the  celestial  sphere,  which  we  may  call  P.  Then 
a  star  lying  in  the  direction  P  or  in  the  opposite  direction 
will  suffer  no  displacement  whatever.  -A  star  lying  in  any 
other  direction  will  be  displaced  in  the  direction  of  the 
point  P  by  an  angle  depending  upon  its  angular  distance 
from  P.    At  90°  from  P  the  displacement  will  be  a  maii- 

mnm. 

Now,  if  the  star  lies  hear  the  pole  of  the  ecliptic,  its  di- 
rection will  always  be  nearly  at  right  angles  to  the  direc- 
tion in  which  the  earth  is  moving.  A  little  consideration 
will  show  that  it  will  seem  to  describe  a  circle  in  conse- 
quence of  aberration.  If,  however,  it  lies  in  the  plane  of 
the  earth's  orbit,  then  the  various  points  toward  which  the 
earth  moves  iu  the  course  of  the  year  all  lying  in  the  eclip- 
tic, and  the  star  being  in  this  same  plane,  the  apparent 
motion  will  be  an  oscillation  back  and  forth  in  this  plane, 
and  in  all  other  positions  the  apparent  motion  will  be  in  art 
ellipse  more  and  more  flattened  as  we  approach  the  ecliptic. 
The  maximum  displacement  of  a  star  by  aberration  is  20'. 44. 

The  connection  between  the  velocity  of  light  and  the  dii*- 
tance  of  the  sun  is  such  that  knowing  one  we  can  infer  the 
other.  Let  us  assume,  for  instance,  that  the  time  required 
for  light  tp  reach  us  from  the  sun  is  498  seqopds,  which 


.-.ai^/.«^w»-  rr^-'■.■-r™»¥w^lnr, 


REFRACTION  AND  ABERRATION  OF  LIGHT.     179 


depend  entirely 

displacement  of 
i  the  aberration 
le  fixed  stars  to 
very  small  orbit. 
Aceived  of  in  thb 
moment,  in  the 
loving  toward  a 
y  call  P.  Then 
pposite  direction 
star  lying  in  any 
direction  of  the 
angular  distance 
t  will  be  a  maii- 

»e  ecliptic,  its  di- 
gles  to  the  dii-ec" 
btle  consideration 
I  circle  in  conse- 
3  in  the  plane  of 
toward  which  the 
ying  in  the  eclip- 
tic, the  apparent 
rth  in  this  pliane, 
Ition  will  be  in  an 
■oach'the  ecliptic. 
ierrationi8  20'.44. 
light  and  the  dii^- 
I  we  can  infer  the 
the  time  required 
)8  secopds,  which 


is  probably  accurate  within  a  single  second.  Then  know- 
ing the  distance  of  the  sun,  we  may  obtain  the  velocity 
of  light  by  dividing  it  by  498.  But,  on  the  other  hand, 
if  we  can  determine  how  many  miles  light  moves  in  a 
second,  we  can  thence  infer  the  distance  of  tlie  sun  by 
multij)lying  it  by  tiie  same  factor.  During  the  lust  cen- 
tury the  distance  of  the  sun  was  found  to  be  certainly  be- 
tween 90  and  100  millions  of  miles.  It  was  therefore 
correctly  concluded  that  the  velocity  of  light  was  some- 
thing less  than  200,000  miles  per  second,  and  probably 
between  180,000  and  200,000.  This  velocity  has  since 
been  determined  more  exactly  by  the  direct  measurements 
at  the  surface  of  the  earth  already  mentioned. 


»fS*=f.'.^.'-^-'--'ft«]«r--^ 


CHAPTER  XII. 


CHRONOLOGY. 


AffiBOKOiaoAL  MBAsntxs  07  Tim. 

The  intimate  relation  of  astronomy  to  the  daily  life  of 
mankind  has  arisen  from  its  aiffording  the  only  reliable  and 
accurate  measure  of  intervals  of  time.  The  fundamental 
units  of  time  in  all  ages  have  been  the  day,  the  month,  and 
the  year,  the  first  being  measured  by  the  revolution  of  the 
earth  on  its  axis,  the  second,  primitively,  by  that  of  the 
moon  around  the  earth,  and  the  third  by  that  of  the  earth 
round  the  sun. 

Of  the  three  units  of  time  just  mentioned,  the  most  nat- 
ural and  striking  is  the  shortest;  namely,  the  day.  It  is 
so  nearly  uniform  in  length  that  the  most  refined  astro- 
nomical observations  of  modern  times  have  never  certainly 
indicated  any  change.  This  uniformity,  and  its  entire 
freedom  from  all  ambiguity  of  meaning,  have  always  made 
the  day  a  common  fundamental  unit  of  astronomers.  Ex- 
cept for  the  inconvenience  of  keeping  count  of  the  great 
oamber  of  days  between  remote  epochs,  no  greater  unit 
would  ever  hwe  been  necessary,  and  we  might  all  date  our 
letters  by  the  nnmber  of  days  after  Chbist,  or  after  any 
other  fixed  date. 

The  difficulty  of  r.^membering  great  numbers  is  such 
that  a  longer  unit  if  absolutely  necessary,  even  in  keeping 
the  reckoning  of  time  for  a  single  generation.    Such  a  unit 


on. 

;he  daily  life  of 
m\j  reliable  and 
be  fundamental 
tbe  montb,  and 
evolution  of  tbe 
by  tbat  of  tbe 
hat  of  the  earth 

d,  the  most  nat- 
tbe  day.  It  is 
tst  refined  astro- 
5  never  certainly 
and  its  entire 
ave  always  made 
bronomers.  Ex- 
int  of  tbe  great 
no  greater  unit 
ight  all  date  our 
18T,  or  after  any 

tumbers  is  snch 
even  in  keeping 
on.    Snob  a  nnit 


CHRONOLOGT. 


181 


is  tbe  year.  Tbe  regular  changes  of  seasons  in  all  extra- 
tropical  latitudes  renders  this  unit  second  only  to  tbe  day 
in  tbe  prominence  with  which  it  must  have  struck  tbe 
minds  of  primitive  man.  These  changes  are,  however,  so 
slow  and  ill-marked  in  their  progress  tbat  it  would  have 
been  scarcely  possible  to  make  an  accurate  determination 
of  the  length  of  the  year  from  tbe  observation  of  tbe  sea- 
sons. Here  astronomicd  observations  came  to  tbe  aid 
of  our  progenitors,  and,  before  tbe  beginnings  of  history, 
it  was  known  that  the  alternation  of  seasons  was  due  to 
the  varying  declination  of  the  sun,  as  tbe  latter  seemed 
to  perform  its  annual  course  among  the  stars  in  the 
"  oblique  circle"  or  ecliptic.  Tbe  seasons  were  also  marked 
by  tbe  position  of  certain  bright  stars  relatively  to  tbe  sun; 
that  is,  by  those  stars  irlsing  or  setting  in  the  morning 
or  evening  twilight.  Thus  arose  two  methods  of  measur- 
ing the  length  of  tbe  year — tbe  one  by  the  time  when  the 
snn  crossed  the  equinoxes  or  solstices;- tlio  other  when  it 
seemed  to  pass  a  certain  point  amoiig  the  Stars;  Atfwis 
have  already  explained,  these  yours  were  8)igiit]y  different, 
owing  to  the  procession  of  the  oquinoUps,.'th0'fir«t  or  equi- 
noctial year  bcinb;  a  Tittle  Ict^s  ami  the  ^fcbiid  dt' sidcrcatl 
year  u  litUo  greater  than  3<)5i4ttys.    . 

Tire  number  of  days  in  n  }'ie«r  is  too  great  to  udmit  of 
their  Wing  easily  rcmembereSi  wiilinnt  iiny  t)roak;Vm 
intermodiutL'  iH»riod  is  tliereforc  ncocKsary.  Such  a,  period 
is  measured  by  the  revolntion  of  tbe  moon  lu^onnd- the 
earth,  or,  more  exactly,  by  the,  recurrence  of  hew  moon, 
which  takes  place,  on  the  average,  at  the  end  of  nearly 
29i  days.  The  nearest  round  number  to  this  is  30  dayf>, 
and  12  periods  of  30  days  ^ch  only  lack  6^  days  of  being 
a  year.    It  has  therefore  been  common  to  consider  a  year 


i    i  i 


;  t 


162 


ASTRONOMT. 


as  made  up  of  12  months,  the  lack  of  exact  correspondence 
being  filled  by  various  alterations  of  the  length  of  the 
month  or  of  the  year,  or  by  adding  surplus  days  to  each 

year.  ,        ,  ,, 

The  true  lengths  of  the  day,  the  month,  and  the  yenr 

having  no  common  divisor,  a  difficulty  arises  in  attempting 
to  make  months  or  days  into  years,  or  days  into  montlis, 
owing  to  the  fractions  which  will  always  be  left  over.  At 
the  same  time,  some  rule  bearing  on  the  subject  is  neces- 
sary in  order  that  people  may  be  able  to  remember  the  yenr, 
month,  and  day.  Such  rules  are  found  by  choosing  some 
cycle  or  period  which  is  very  nearly  an  exact  number  of 
two  units,  of  months  and  of  days  for  example,  and  by 
dividing  this  cycle  up  as  evenly  as  possible. 

POBKATIOir  OT  CAUHDAXB. 

The  montlis  now  or  heretofore  in  use  among  the  peoples  of  the 
dolKs  may  for  the  most  part  be  divided  Into  two  classes. 

(1)  The  lunar  month  pure  and  simple,  or  the  mean  interval  be- 
tween successive  new  moons. 

(2)  An  approximation  to  the  twelfth  part  of  a  year,  wilhout  respect 
to  the  motion  of  the  moon. 

Tlw  lunar  Month. -Tlie  mean  Interval  iK-tween  consecutive  new 
moons  beinir  nearly  20i  days.  It  was  conmu.ti  in  llic  use  of  the  pure 
lunar  month  to  have  months  of  29  and  30  days  aliernUcly.  This 
supposed  perloil.  however,  will  fall  short  by  a  day  in  ah(,ut  2i  years. 
Tills  defect  was  remedied  by  Introducing  cycles  containing  rather  more 
months  of  80  than  of  29  .lays,  the  small  excess  «.f  long  months  being 
spread  uniformly  through  the  cycle.  Thus  the  Greeks  »"«l  «  «"y«>« 
of  aaa  months,  of  which  125  were  full  or  long  months,  and  110  were 
short  or  deficient  ones.  We  see  that  the  length  of  this  cycle  was 
8940  days  (125  X  80  +  110  X  29).  whereas  the  length  of  285  true  lunar 
months  is  285  X  29.58088  =  6989.688  days.  The  cycle  was  therefore 
too  lone  by  less  than  one  third  of  a  day.  and  the  error  of  count  would 
amount  to  only  one  day  in  more  than  70  years.  The  Mohammedan^ 
«nin.  took  »  cycle  of  860  months,  which  they  divided  into  169  short 
Sdm  tongones.    The  length  of  thU  cycle  wm  10681  days,  whUe 


Borrespondonce 
length  of  the 
18  days  to  each 

I,  and  the  year 
s  in  attempting 
fs  into  montlis, 

left  over.  At 
ubjoct  is  neces- 
ember  the  year, 

choosing  some 
cact  number  of 
cample,  and  by 


(he  peoples  of  tlie 

asses; 

meuu  interval  be- 

sar,  wilhoiUri'spect 

n  consecutive  new 
lite  use  of  tlic  pure 
iilternUcly.  Tliis 
'  ill  about  2i  years, 
tiiiningriitliernioro 
long  months  licing 
Greeks  had  a  cycle 
inths,  and  110  wcro 
li  of  this  cycle  was 
th  of  285  true  lunar 
cycle  was  therefore 
rror  of  count  would 
%e  Mohammedans, 
vided  into  100  short 
B  10681  days,  'while 


OBSONOLOOT. 


188 


the  true  length  of  890  lunar  months  is  10081.018  days.  The  count 
would  tlierefore  not  be  a  day  in  error  until  the  end  of  about  80 
cycles,  or  nearly  23  centuries.  This  month  therefore  follows  the 
moon  closely  enough  for  all  praclical  purposes. 

Months  other  than  Loaar.— The  complications  of  the  system  Juat 
described,  aud  the  consequent  ditficuliy  of  making  the  calendar 
month  represent  the  course  of  the  moon,  are  so  great  that  the  purs 
luuar  month  was  generally  abandoned,  except  among  people  whose 
religion  ruquircd  Important  ceremonies  at  the  time  of  new  moon.  In 
such  cases  the  year  has  been  usually  divided  into  12  months  of 
slightly  different  lengths.  The  ancient  Egyptians,  however,  had  12 
mouths  of  aO  days  each,  to  which  they  added  5  supplementary  days 
at  the  close  of  each  year. 

Kinds  of  Tear.— As  we  find  two  different  systems  of  months  to 
have  been  used,  so  we  may  divide  the  calendar  years  into  thne 
classes,  namely: 

(1)  The  lunar  year,  of  12  lunar  months. 

(8)  The  solar  year. 

(ji)  The  combined  luni-solar  year. 

Ths  Luar  Tosx.— We  have  already  called  attention  to  the  fact  that 
the  time  of  recurrence  of  the;  year  is  not  well  marked  except  hj 
astronomical  phenomena  which  the  casual  observer  would  haidlj 
remark.  But  the  time  of  new  moon,  or  of  beginning  of  the  month, 
is  always  well  marked.  Consequently  it  was  very  natural  for  people 
to  begin  by  considering  the  year  as  made  up  of  twelve  lunations,  the 
error  of  eleven  days  being  unnoticeable  in  a  single  year  unless  can* 
f  ul  astronomical  observations  were  made.  Even  when  tliis  error  was 
fully  recognized,  it  might  be  considered  better  to  use  the  regular 
year  of  12  lunar  months  than  to  use  one  of  an  Irregular  or  Tuying 
number  of  months.    The  Moliammedans  use  such  a  year  to  this  day. 

Thi  Bolar  Tsar.— In  forming  this  year,  the  attempt  to  meesarethe 
year  by  revolutions  of  tlie  moon  is  entirely  abandoned,  aud  its  length 
is  made  to  depend  entirely  on  the  change  of  the  seasons.  The  solar 
year  thus  indicated  is  that  nrost  used  in  both  ancient  and  modem 
times.  Its  length  has  been  'rtjown  to  be  nearly  865^  days  from  the 
timesof  the  earliest  iMtronc^^'x,  and  the  system/idopted  in  onr  cal- 
endar of  having  three  years  of  165  days  each,  followed  by  one  of  806 
days,  has  been  employed  in  China  from  the  remotest  historic  times. 
Tliis  year  of  865^  days  is  now  called  by  us  the  Julian  Ttar,  after 
Jin.n;s  GisaAB,  from  whom  we  obtained  it. 

The  Voteaie  Oydo.— These  considerations  will  enable  ns  to  under* 
stand  the  origin  of  our  own  calendar.  We  begin  whh  the  Hetonic 
Cyide  of  the  andent  O.rseks,  which  still  regulates  some  reHgioutfes- 


-  -f^5^'-.;«--?^>  :f  i"»C1;-ir.'T-*^ 


184 


ABTRONOMT. 


tivftli,  although  it  hM  dinppeared  from  our  civil  reckoning  of  time. 
The  neceisity  of  employing  lunar  months  osused  the  Greeks  great 
ilifflculty  in  regulating  tlieir  calendar  so  as  to  accord  with  their  rules 
for  religious  feasts,  until  a  solution  of  the  problem  was  found  by 
Meton,  about  488  b.c.  The  discovery  of  Metom  was  that  a  period 
or  cycle  of  6040  days  could  lie  divided  up  into  285  lunar  months,  and 
also  into  10  solar  years.  Of  these  months,  125  were  to  be  of  80  days 
each  and  110  of  20  days  each,  which  would,  in  all,  make  up  the  re- 
quired 6040  days.  To  see  how  nearly  this  rule  represents  the  actual 
motions  of  the  sun  and  moon,  we  remark  that: 

Days.  Hours.  MIn. 

885  lunations  require 6080           16  81 

10  Julian  years  require 6080          18  0 

10  true  solar  years  require 6080          14  27 

We  see  that  though  the  cycle  of  6040  days  is  a  few  hours  too 
long,  yet  if  we  take  285  true  luirnr  months,  we  find  their  whole  dura- 
tion to  bo  a  little  less  tiian  10  Julian  years  of  865^  days  each,  and  a 
little  more  than  10  true  solar  years. 

The  problem  was  to  take  these  285  months  and  divide  them  up 
into  10  years,  of  which  12  should  have  12  months  each  and  7 
should  have  18  months  each.  Tiie  long  years,  or  those  of  13  months, 
were  probably  those  corresponding  to  the  numbers  8,  5, 8,  11,  18, 16, 
and  10,  while  tiie  first,  second,  fourth,  sixth,  etc.,  were  short  yeara. 
In  general,  the  montlis  bad  M  and  80  days  alternately,  but  it  was 
necessary  to  substitute  a  long  month  for  a  short  one  every  two  or 
three  years,  so  tiiat  in  the  cycle  there  should  he  125  long  and  110 
aiiort  months. 

Ooldm  Vuibtr.— This  ia  simply  the  number  of  the  year  in  the 
Motonic  Cycle,  and  is  said  to  owe  its  appellation  to  the  enthusiasm 
of  tiie  Oreeks  over  Mbtom'b  discovery,  the  authorities  having  ordered 
tlie  division  and  numbering  of  the  years  in  the  new  calendar  to  be 
inscribed  on  public  monuments  in  letters  of  gold.  The  rule  for  find- 
ing the  golden  numlier  is  to  divide  tlie  number  of  the  year  by  10  and 
add  1  to  the  remainder.  From  1881  to  1800  it  may  be  found  by  sim- 
ply subtracting  1480  from  the  year.  It  is  employed  in  our  church 
calendar  for  finding  the  time  of  Easter  Sunday. 

The  jraliaa  Oaleadar.— The  civil  calendar  now  in  use  throughout 
Christendom  had  its  origin  among  the  Romans,  and  its  foundation 
was  laid  by  Jclics  CiHSAB.  Before  hfai  time,  Rome  can  hardly  be 
said  to  have  hvA  a  chronological  system,  the  length  of  the  year  not 
being  prescribed  by  any  invariable  rule,  and  being  therefore  changed 
from  time  to  time  to  auit  the  caprice  Or  to  omnpua  the  endt  of  the 


CBttONOtOOY. 


18» 


;koDiDg  of  time, 
be  Greeks  great 
with  their  rules 
in  was  found  by 
as  that  a  period 
nar  moDtlis,  and 
to  be  of  80  days 
make  up  the  re- 
sents the  actual 


lours.  MIn. 

16  81 

18  0 

14  27 

few  lioura  too 
leir  whole  dura- 
ays  each,  and  a 

divide  them  up 
lis  each  and  7 
le  of  18  months, 
5. 8.  11.  18. 16, 
ere  short  years, 
tely,  but  it  was 
le  every  two  or 
M  long  and  110 

the  year  in  the 
the  enthusiasm 
having  ordered 
calendar  to  be 
he  rule  for  find- 
I  year  by  19  and 
e  found  by  sim> 
1  in  our  church 

use  throughout 
;  its  foundation 
i  can  hardly  be 
of  the  year  not 
erefore  changad 
the  endtof  the. 


rulers.  Instances  of  tliis  tampering  disposition  ore  familiar  to  the 
hitturical  student.  It  is  said,  for  instance,  tliat  the  Oauls  having  to 
pay  a  certain  monthly  tribute  to  tlie  Romans,  one  of  tlie  governors 
ordered  the  year  to  be  divided  into  14  months,  in  order  lliat  tlio  pay 
days  might  recur  more  rapidly.  A  year  was  fixed  at  865  days,  with 
the  addition  of  one  day  to  every  fourth  year.  The  old  Roman  months 
were  afterward  adjusted  to  the  Julian  year  in  such  a  way  as  to  give 
rise  to  the  somewliat  irregular  arrangement  of  months  which  wo  now 
have. 

Old  aaA  Xew  Itylas.— Tlie  mean  length  of  the  Julian  year  is  865} 
days,  about  11}  minutes  greater  than  that  of  tlie  true  equinoctial 
year,  which  measures  the  recurrence  of  the  seasons.  This  difference 
is  of  little  practical  importance,  as  it  only  amounts  to  a  week  in  a 
thousand  years,  and  a  change  of  this  amount  in  that  period  is  pro- 
ductive of  no  inconvenience.  But,  desirous  to  iiave  the  year  as  cor- 
rect as  possible,  two  changes  were  introduced  into  the  calendar  by 
Pope  Oreoory  XIII.  with  this  object.    They  were  as  follows  : 

(1)  The  day  following  October  4,  1582,  was  called  the  15th  instead 
of  the  Sth,  thus  advancing  the  count  10  days. 

(2)  The  closing  year  of  each  century.  1600,  1700,  etc.,  instead  of 
being  always  a  leap-year,  as  in  the  Julian  ciilendar.  is  such  only 
when  the  number  of  the  century  is  divisible  by  4.  Tlius  while  1600 
remained  a  leap-year,  as  before.  1700,  1800,  and  liMO  were  to  be 
common  years. 

This  change  in  the  calendar  was  speedily  adopted  by  all  Catholic 
countries,  and  more  slowly  by  Protestant  ones,  England  holding  out 
until  1752.  In  Russia  it  has  never  Iteen  adopted  at  all.  the  Julian 
calendar  being  still  continued  without  change.  The  Russian  reckon- 
ing is  therefore  12  days  behind  ours,  the  ten  days  dropped  in  1582 
being  increased  by  the  days  dropped  from  the  years  1700  and  1800  in 
the  new  reckoning.  This  modified  calendar  is  called  the  Oregorian 
OaUndar,  or  Ifeu  l^te,  while  the  old  system  is  called  the  JuUan 
QOendar,  or  OM  Style. 

It  is  to  be  remarked  that  the  practice  of  commencing  the  year  on 
January  let  was  not  universal  until  comparatively  recent  times.  The 
most  common  times  of  commencing  were.  perlAipa.  March  1st  an<l 
March  22d.  the  latter  being  the  time  of  the  vernal  equinox.  But 
January  1st  gradually  made  its  way,  and  became  universal  after  its 
adoption  by  England  in  1752. 

lolar  OyeU  aai  Deaiaieal  Letter.^In  our  church  calendars  Janu- 
ary 1st  is  marked  by  the  letter  A.  January  2d  by  B,  and  so  on  to  O. 
when  the  seven  letters  begin  over  again,  and  are  repeated  througli 
the  year  In  the  same  order.   Each  letter  there  indioptea  the  same  day 


-J 
■J 


,1 


186 


A8TH0N0M7. 


of  the  we«k  throughout  each  separate  year,  A  Indicating  the  day  on 
which  January  Ist  falls,  1)  tiic  (lay  following,  nnd  bo  on.  An  excep- 
tion occurs  in  leap  yeant,  when  Februiiry  20lh  und  Mitn^h  1st  are 
murl(ed  by  the  same  letter,  so  that  a  change  occurH  at  the  Ijeginning 
of  March.  The  letter  corresponding  to  Sunday  ou  tliis  scheme  is 
called  the  Dotninieal  or  Sunday  letter,  and  when  we  once  linow 
what  letter  it  is,  ull  the  Sundays  of  the  year  are  indicateil  by  that 
letter,  and  hence  all  the  other  diiys  of  llie  week  by  their  letters.  In 
leap-years  there  wdl  be  two  Dumiuicul  letters,  that  fur  the  lu(*t  ten 
months  of  the  year  lieing  the  one  next  preceding  the  letter  for 
January  and  February.  In  the  Julian  calendar  the  Dominical  letter 
must  always  recur  at  the  end  of  28  years  (besides  three  recurrences 
at  unequal  intervals  in  the  mean  time).  Tliis  period  is  called  the 
lolar  eyele,  and  determines  the  days  of  the  week  on  which  the  days 
of  the  month  fall  during  cacli  year. 

Since  any  day  of  any  year  occurs  one  day  later  in  the  week  tlian 
it  did  the  year  before,  cr  two  dnys  later  when  a  20tk  of  February 
haa  intervened,  the  Dominical  letters  recur  in  the  order  O,  F,  £,  D, 
C,  B,  A,  O,  etc.  This  muy  also  be  expressed  by  saying  that  any  day 
of  a  past  yeor  occurn!d  one  day  earlier  in  the  week  for  every  year 
that  has  elapsed,  and,  in  addition,  one  day  earlier  for  every  29lh  of 
February  that  has  intervened.  This  fact  will  make  it  easy  to  calcu- 
late the  day  of  the  week  ou  which  any  historictU  event  happened 
from  the  day  corresponding  in  any  past  or  future  year.  Let  us  take 
the  following  example: 

On  what  day  of  the  week  was  WAsniNnTON  born,  the  date  being 
1782,  February  22d,  knowing  that  February  22d,  1879,  fell  on 
Saturday?  The  interval  is  147  years:  dividing  by  4  we  have  • 
quotient  of  86  and  a  remainder  of  8,  showing  that,  had  every  fourth 
year  in  the  interval  been  a  leap-year,  there  were  either  86  or  87  lenp- 
yoars.  Aa  a  February  29th  followed  only  a  week  after  the  date,  the 
numlier  must  be  37;*  but  as  1800  was  dropped  from  the  list  of  leap- 
years,  the  number  was  really  only  86.  Then  147  -|-  86  =  188  days 
advanced  in  the  week.  Dividing  by  7,  because  the  same  day  of  the 
week  recurs  after  seven  days,  we  find  a  remainder  of  1.  So 
February  22d,  1879,  is  one  day  further  advanced  than  was  Febru- 
ary 22d,  1782;  so  the  former  being  Snturday,  Wabhinotom  was  bom 
on  Friday. 


*  Perhaps  the  moat  convenient  mr"  of  deciding  whether  the  remainder  does 
or  does  not  indicate  an  additional  leap-year  it  to  subtract  it  from  the  last  date, 
and  see  whether  a  February  S9th  then  intervenes.  Subtracting  8  years  from 
February  SM,  1879,  we  have  February  iMd  187S,  and  a  SVth  oooura  ItetweeB  tbe 
twdJdaMii  oidir  a- week  after  the  first 


CUR0N0L0Q7. 


vn 


sating  the  day  oil 
DO  on.  An  excep- 
1(1  March  lit  are 
at  the  beginning 
lu  this  scheme  is 
II  wo  once  know 
indicated  by  that 
'  their  Ivtturs.  In 
It  for  the  la«t  ten 
ng  the  letter  for 
;  Dominical  letter 
three  recurrences 
criod  is  called  the 
n  which  the  days 

in  the  week  than 
2Qthof  February 
»rder  O,  P,  E,  D, 
yiug  that  any  day 
ek  for  every  year 
•  for  every  29lh  of 
e  it  easy  to  calcu- 
1  event  happened 
■ear.    Let  us  take 

n,  the  date  being 
8d,  1879,  fell  on 
l)y  4  we  have  a 

bad  every  fourth 
her  86  or  87  leap- 
after  the  date,  the 
n  the  list  of  leap- 
+  86  =  188  days 
B  same  day  of  the 
inder  of  1.     So 

than  was  Febru- 
[iNOTON  was  bom 


the  remainder  does 
t  from  the  last  date, 
ictlng  S  years  from 
oooura  betweeo  tbe 


Simiov  Of  Tn  Day. 

The  division  of  the  day  into  hours  was,  in  ancient  and  mediaval 
times,  effected  in  a  way  very  different  from  that  which  we  practise. 
Artiflcial  timekeepers  not  lieing  lu  general  use,  the  two  funda- 
mental moments  were  sunrise  and  si'usct,  wliich  marked  the  day  u 
distinct  from  the  night.  The  first  subdivision  of  this  interval  was 
marked  by  the  instant  of  noon,  when  tlie  sun  was  on  the  meridian. 
The  day  was  thus  subdivided  into  two  parts.  The  night  was 
similarly  divided  by  the  times  of  rising  and  culmination  of  the 
various  constellations.  Edhipiues  (486-407  a.c.)  makes  the  chorus 
in  Jtlutui  ask : 

"  Chorus.— Whose  Is  the  guard?  Who  takes  my  turnT  Theflnt 
iifftu  are  tetting,  and  the  teveu  IHtUuU*  are  in  the  $ky,  and  the  Eagle 
glidee  midvajf  through  heaten.  Awake!  Why  do  you  delay T  Awake 
from  your  beds  to  watch  I  See  ye  not  the  brilliancy  of  the  moonT 
Morn,  morn  indeed  is  approaching,  and  hWier  U  one  o/  the  forerun- 
ning ttari." 

The  interval  between  sunrise  and  sunsti  was  divided  Into  twelve 
equal  parts  called  hours,  and  as  this  Interval  varied  with  the  season, 
the  length  of  the  hour  varied  also.  The  night,  whether  long  or 
short,  was  divided  Into  hours  of  the  same  character,  only  when  the 
niglit  hours  were  long  those  of  the  day  were  short,  and  viee  tena. 
These  variable  hours  were  called  temporary  hour;  At  the  time  of 
the  equinoxes  both  the  day  and  the  night  hours  were  of  the  same 
length  with  those  we  use;  namely,  the  twenty-fourth  part  of  the 
day;  these  were  therefore  called  equinaetial  hourt. 

Instead  of  commencing  the  civil  day  at  midnight,  as  we  do.  It  was 
customary  to  commence  it  at  sunset.  The  Jewish  Sabbath,  for 
instance,  commenced  as  soon  as  the  sun  set  on  Friday,  and  ended 
when  it  set  on  Saturday.  This  made  a  more  disUnctive  di  .'ision  of 
the  astronomical  day  than  that  which  we  employ,  and  led  naturally 
to  considering  the  day  and  the  nigM  aa  two  distinct  periods,  each  to 
be  divided  into  12  hours. 

So  long  as  temporary  hours  were  used,  the  beginning  of  the  day 
•nd  the  beginning  of  the  night,  or,  as  we  should  call  it,  sis  o'clock 
in  the  morning  and  six  o'clock  in  the  evening,  were  marked  by  the 
rising  and  setting  of  the  sun;  but  when  eqainoctial  hours  were 
introduced,  neither  sunrise  nor  sunset  oould  be  taken  to  count  from, 
because  both  varied  too  much  in  the  coarse  of  the  year.  It  therefore 
became  customary  to  count  from  noon,  or  the  time  at  which  the  sun 
pteed  the  meridian.    The  old  habit  of  dividlnf  the  daf  i 


Tgsaaiait^., 


188 


ASmONOMY. 


night  each  into  12  parts  was  continued,  the  first  13  being  reclconed 
from  midniglit  to  noon,  and  the  second  from  noon  to  midnight.  The 
day  was  made  to  commence  at  midnight  rather  than  at  noon  for 
obvious  reasons  of  convenience,  aithougli  noon  was  of  course  the 
point  at  whicii  tlie  time  had  to  be  determined. 

.  Equation  of  Time.— To  any  one  who  studied  the  annual  motion  of 
the  sun,  it  must  liuve  t)een  quite  evident  tliat  the  intervals  lietween 
it^  successive  passages  over  tiie  meridian,  or  l)etween  one  noon  ind 
tlie  next,  could  not  \»  the  same  throughout  tlie  year,  Iiecsuse  tlie 
apparent  motion  of  the  suja  in  right  ascension  is  not  constant,  It 
will  \m  rememliered  that  the  apparent  revolution  of  the  starry 
sphere,  or,  which  is  the  same  thing,  the  diurnal  revolution  of  the 
earth  upon  its  axis,  may  lie  regarded  as  aI)Roiutcly  constant  for  all 
practical  purposes.  This  revolution  is  measured  around  in  right 
ascension  as  explained  in  tlie  opening  chapter  of  this  worlE.  If  the 
sun  increased  its  right  ascension  by  the  same  amount  every  day,  it 
would  pass  the  meridian  S"*  58*  .later  every  day,  as  measured  by 
sidereal  time,  and  hence  tlie  intervals  between  successive  passages 
would  l)e  equal.  But  tlie  motion  of  the  sun  in  right  ascension  is 
unequal  from  two  causes:  (1)  the  unequal  motion  of  the  earth  in  its 
annual  revolution  around  it,  arising  from  tlie  eccentricity  of  the 
earth's  orbit,  and  (2)  the  obliquity  of  the  ecliptic.  How  the  first 
cause  produces  an  inequality  is  obvious.  The  mean  motion  is  8"  56*; 
the  actual  motion  varies  from  8"  4S*  to  4»  4*. 

The  effect  of  the  obliquity  of  the  ecliptic  is  still  greater.  When 
the  sun  is  near  the  equinox,  tlie  direction  of  its  motion  along  the 
eclipt\c^  makes  an  angle  of  28^°  with  the  parallels  of  declination, 
since  its  motion  in  right  ascension  is  measured  along  the  parallel  of 
decliniition,  we  see  tliat  it  is  less  than  tlie  motion  in  longituue.  The 
days  are  then  20  seconds  shorter  than  they  would  be  were  there  no 
obliquity.  At  the  solstices  the  opposite  effcqt  is  produced.  Here 
the.  different  n^eridians  of  right  ascension  are  nearer  together  than 
they  are  at  the  equator;  when  the  sun  moves  through  one  degree 
along  the  ^ciiplic,  it  changes  its  right  ascension  by  l°-08;  here, 
therefore,  tlie  days  are  about  19  seconds  longer  than  they  would  be 
if  the  obliquity  of  the  ecliptic  were  zero. 

We  thus  have  to  recognize  two  slightly  different  kinds  of  days: 
a^r  days  and  mean  days.  A  solar  day  is  the  interval  of  time 
between  two  successive  transits  of  the  sun  over  the  same  meridian, 
wliile  a  mean  day  is  the  mean  of  all  the  solar  days  in  a  year.  If  we 
h^  two  clocks,  one  going  with  perfect  uniformity,  but  regulated 
8Q  as  to  keep  as  near  the  sun  as  possible,  and  the  other  changing  its 
n^te  8Q  as  to  alwiqrs  follow  the  sun,  the  latter  would  gain  or  low  oq 


3  being  reckoned 

0  midnight.  TLe 
than  at  noon  for 
as  of  course  the 

tnnuftl  motion  of 
ntervals  between 
len  one  noon  nnd 
^ear,  Iiecsuse  the 
not  constant,  It 
in  of  the  starry 
revolution  of  the 
constant  for  all 
around  in  right 
Ills  work.  If  the 
unt  every  day,  it 
as  measured  by 
ccessive  passages 
right  ascension  is 
f  the  earth  in  its 
centricity  of  the 
.  How  tlie  first 
motion  is  8"  56*; 

1  greater.  When 
notion  along  the 
Is  of  declination, 
(ig  the  parallel  of 
1  longituue.  The 
be  were  there  no 
produced.  Here 
rer  together  than 
ough  one  degree 

by  l°-08;  here, 
in  they  would  be 

tt  kinds  of  days: 
interval  of  time 
e  same  meridian, 
in  a  year.  If  we 
ty,  but  regulated 
ther  changing  its 
d  gain  or  Iom  oq 


onnoKOLOor. 


ISd 


the  former  by  amounts  sometimes  rising  to  22  seconds  in  a  day.  The 
accumulation  of  these  variatious  through  a  period  of  several  months 
would  lead  to  such  deviations  that  the  suii-clock  would  be  A  minutes 
slower  than  the  other  during  the  first  half  of  February,  anvl  16 
minutes  faster  during  the  first  week  in  November.  The  time-kceiicrs 
formerly  used  were  so  imperfect  that  tliese  inequalities  in  the  solar 
day  were  nearly  lost  in  the  necessary  irregularities  of  the  rate  of  the 
clock.  All  clocks  were  therefore  set  by  the  sun  as  often  as  was 
found  necessary  or  convenient.  But  during  the  last  century  it  was 
found  by  astronomers  tliat  the  use  of  unite  of  time  varying  in  this 
way  led  to  much  inconvenience;  they  therefore  substituted  mean 
time  for  solar  or  apparent  time. 

Mean  time  is  so  measured  that  the  hours  and  days  shall  always  be 
of  the  same  length,  and  shall,  on  the  average,  be  as  much  behind  the 
sun  as  ahead  of  it  We  may  imagine  a  fictitious  or  mean  sun  mov- 
ing along  the  equator  at  the  rate  of  8"  66*  in  right  ascension  every 
day.  Mean  time  will  then  be  measured  by  the  passage  of  this 
fictitious  sun  across  the  meridian.  Apparent  time  was  used  in 
ordinary  life  after  it  was  given  up  by  astronomers,  because  it  ^as 
very  easy  to  set  a  clock  from  time  to  time  as  the  sun  passed  a  nopp- 
mark.  But  when  the  clock  was  so  far  improved  that  it  kept  much 
better  time  than  the  sun  did,  it  was  found  troublesome  to  keep  put- 
ting it  backward  and  forward  so  as  to  agree  with  the  sun.  Thus 
mean  time  was  gradually  introduced  for  all  the  purposes  of  ordinary 

The  common  household  almanac  should  give  the  equation  of  time, 
or  the  mean  time  at  which  the  sun  passes  the  meridian,  on  each  day 
of  the  year.  Then,  if  any  one  wishes  to  set  his  clock,  he  knows  the 
moment  when  the  sun  passes  the  meridian,  or  when  it  is  at  some  noon- 
mark,  and  sets  his  time-piece  accordingly.  For  all  purposes  where 
accurate  time  is  required,  recourse  must  be  had  to  astronomical 
observation.  It  is  now  customary  to  send  time-signals  every  day  at 
noon,  or  some  other  hour  agreed  upon,  from  observatories  along  tlic 
principal  lines  of  telegraph.  Thus  at  the  present  time  the  momont 
of  Washington  noon  is  signalled  to  New  York,  and  over  the  principiil 
lines  of  railway  to  the  South  and  West.  Each  person  within  reach 
of  a  telegraph-oflSce  can  then  determine  his  local  time  by  correcting 
these  signals  for  the  difference  of  longitude. 


^mim 


PAET  II 

THE  SOLAR  SYSTEM  IN  DETAIL 


III 


i!;i. 


CHAPTER  I. 

STRUCTURE  OP  THE  SOLAR  SYSTEM. 

The  solar  system  consists  of  the  sun  as  a  central  body, 
MTOund  which  revolve  the  major  and  minor  planets,  with 
their  satellites,  a  few  periodic  comets,  and  an  iinknown 
number  of  meteor  swarms.  These  are  permanent  members 
of  the  system.  At  times  other  comets  appear,  and  move 
nsnally  in  parabolas  through  the  system,  around  the  sun, 
and  away  from  it  into  space  again,  thus  visiting  the  system 
without  being  permanent  members  of  it. 

The  bodies  of  the  syatem  may  be  classified  as  follows : 

1.  The  central  body — the  Sun. 

8.  The  four  inner  planets — Mercury,  Venut,  the  Earth,  Mart. 

8.  A  group  of  small  planets,  sometimes  called  Aiteroidt,  reTolTing 
outside  of  the  orbit  of  Mars. 

4  A  group  of  four  outer  planets— /upi^,  Saium,  Uranu»,  and 
Neptune. 

6.  The  satellites,  or  secondary  bodies,  revolving  about  the  planets, 
their  primaries. 

6,  A  number  of  comets  and  meteor  swarms  revolving  in  very 
eccentric  orbits  about  the  sun. 

The  eight  planets  of  Groups  8  and  4  are  sometimes  classed  to> 
gether  as  the  nu^  planett,  to  distinguish  them  from  the  two  hun- 
dred or  more  minor  planett  of  Group  8.  The  formal  dafinitions  of 
the  various  classes,  laid  down  by  Sir  Wiluax  Hbbsohbl  in  1808,  ara 
worthy  of  repetition : 


FAIL 


rSTEM. 

I  a  central  body, 
lor  planets,  with 
ad  an  unknown 
manent  members 
ppear,  and  move 
around  the  sun, 
siting  the  system 

ollows : 

e  Earth,  Mar$. 
Atteroidi,  revolving 

atum,  Uranut,  aod 

g  about  the  planets, 

revolving  in  very 

metimes  classed  to- 
from  the  two  hun- 
srmal  dafinitions  of 
owcHBL  in  1800,  am 


arnucTURE  of  the  solar  system.       191 

Planets  are  celestial  bodies  of  a  certain  very  considerable  slee. 
They  move  in  not  very  eccentric  ellipses  about  the  sun.  The  planes 
of  their  orbits  do  not  deviate  many  degrees  from  the  plane  of  the 
earth's  orbit.  Their  motion  about  the  sun  is  direct  (from  west  to 
east).    They  may  have  satellites  or  rings.    They  have  atmospheres  of 


I  ! 


Fia.  S6w— Raunvi  Soiricaa  or  nn  FUMifs. 

considerable  extent,  which,  however,  bear  hardly  any  sensible  pro. 
portion  to  their  diameters.  Their  orbito  are  at  certain  considerabhi 
distances  from  each  other. 

AstereUs,  now  more  generally  known  as  maatt  or  minor  pfoMtt,  are 
oekstial  bodies  which  move  about  the  sun  in  orbiU,  «iUier  of  little  or 


199 


ASTRONOMY. 


of  considerable  eccentricity,  the  planes  of  which  orbits  maj  be  in- 
clined to  the  ecliptic  nt  any  angle  whatsoever.  They  may  or  may 
not  have  considerable  atmospheres. 

OomeU  are  celestial  bodies,  generally  of  a  very  small  mass,  though 
how  far  this  may  be  limited  is  yet  unknown.    Tliey  move  in  very 


*!l 


Tm.  M.— Aptabxmt  M Aomnrou  or  thb  Scm  as  bbkn  raoii  Dmnaumr  Fbimn. 

eccentric  ellipses  or  in  parabolic  arcs  about  the  t'Un.  The  planes  of 
their  motion  admit  of  the  greatest  variety  in  their  situation.  Tlw 
direction  of  their  motion  is  also  totally  undetermined.  They  liaTe 
atmospheres  of  very  great  «xtent,  which  sliow  themselvos  in  vaH<Ml 
fonns  as  tails,  com*,  lutsin^ss.  etc. 


ih  orbits  maj  be  in- 
They  may  or  may 

small  mass,  though 
Tliey  move  in  very 


BM  DmnaumT  FLiim*. 

hvm.  The  planes  of 
heir  situation.  The 
irmined.  They  liaTe 
lie  cueKee  in  TarhMM 


BTBUCTURB  OF  THE  80LAR  SYSTEM. 


193 


BalatiTe  InrilMss  of  tha  Planets. — The  comparative  surfaces  of  the 
major  planets,  as  they  would  appear  to  an  observer  situated  at  an 
equal  distance  from  all  of  them,  is  given  in  the  figure  on  page  191. 

The  relative  apparent  magnitudes  of  the  sun,  as  seen  from  the 
various  planets,  is  shown  in  the  figure  on  page  192. 

Flora  and  Mnemo»yM  are  two  of  the  asteroids. 

A  curious  relation  between  the  distances  of  the  planets,  known  as 
Bodb'8  law,  deserves  mention.    If  to  the  numl)ers 
0,  8,  «,  la.  24.  48,  98,  193,  884, 
each  of  which  (the  second  excepted)  is  twice  the  preceding,  we  add 
4,  we  obtain  the  series 

4,  7,  10,  16,  28,  62, 100,  196,  888. 

These  last  numbers  represent  approximately  the  distances  of  the 
planets  from  the  sun  (except  for  Neptune,  which  was  not  discovered 
when  the  so-called  law  was  announced). 

This  is  shown  in  the  following  table : 


Plakbts. 


Mercury. 
Venus. . . 
£»):th. . . . 
Mars 

S Ceres]. . 
upiter. . 
Saturn . . , 
Uranus. . 
Neptune. 


Actuid 
Distance. 

BoDa*s  Law. 

8-9 

40 

7-2 

70 

100 

100 

16-3 

,  160 

27-7 

280 

52'0' 

62'© 

95-4 

lOOi*  ' 

191. 8 

i960 

800-4 

888  0    ., 

It  will  be  observed  that  Neptune  does  not  fall  within  this  ingfnioiil 
scheme.    CerfB  is  one  of  the  minor  planets. 

The  relative  brightness  of  the  son  and  the' various  plan^frtu  has  been 
measured  by  ZOllrbb.  and  tiM  results  are  given  below.  Tlie  column 
per  eeiit  shows  the  percentage  -of  error  indicated  in  the  separate  re- 
snlU:  : . 


Om  Am 

BaUoMto 

Percent  of  ErroA 

Moon 

618.000 

6,994.000,000 

6.473.000,000 

180,980,000,000 

8.486.000,000,000 

79,690,000.000,000 

.      16 

Mars..... 

6-8         . 

Juirfter 

6.7 

Saturn  (tell  alone). 

Uranus '•... 

60 
60 

Neptune 

65 

^■i 


194 


ASTSONOMT. 


; 


\i 


The  differancm  in  the  density,  sise.  mHa,  and  diitance  of  the 
Mveral  plkuets,  and  in  the  amount  of  solar  llglit  and  lieat  which  they 
receive,  are  immense.  The  distance  of  Xeptune  is  eighty  times  that 
of  Mercury,  and  it  receives  only  j^  as  much  light  and  heat  from  the 
sun.  Tlie  density  of  the  earth  is  about  six  times  that  of  water,  while 
Saturn'$  mean  density  is  less  than  that  of  water. 

The  mass  of  tlie  sun  is  far  greater  than  that  of  any  single  planet 
in  the  system,  or  indeed  than  tlie  combined  mass  of  all  of  them.  In 
general,  it  is  a  remarkable  fact  that  the  mass  of  any  given  planet  ex- 
ceeds the  sum  of  the  masses  of  all  the  planets  of  less  mass  than  itself. 
Tills  is  shown  in  the  following  table,  where  the  masses  of  the  planets 
are  taken  as  fractions  of  the  sun's  mass,  which  we  here  express  as 
1,000,000,000: 


I 

1 

1 

1 

o 

1 

1 

! 

1 

FbAinm. 

MO 

as4 

s,su 

8,000 

M,aao 

Bl,fl0O 

»B,880 

gB4.aoB 

1,000,000,000 

Mswes. 

The  total  mass  of  tiie  small  planets,  like  their  number,  is  unknown, 
but  it  is  probably  less  than  one  thousandth  that  of  our  earth,  and 
would  hardly  increase  the  sum-total  of  the  above  masses  of  the  solar 
system  by  more  than  one  or  two  units.  The  sun's  mass  is  thus  over 
TOO  times  that  of  all  the  other  liodies,  and  hence  the  fact  of  its  cen- 
tral position  in  the  solar  system  is  explained.  In  fact,  the  centre  of 
gratilyol  the  whole  solur  system  is  very  little  outside  the  Irady-of  the 
sun,  and  will  lie  inside  of  it  when  Jupiter  and  Saturn  are  in  opposite 
direct  ions  from  it. 

f  laastary  Aspeets. — Tiie  motions  of  the  planets  about  the  sun  have 
lieen  explained  in  Chapter  Y.  From  what  is  there  said  it  appears 
that  tlie  best  time  to  see  one  of  the  outer  planets  will  be  when  it  is 
in  opposition;  that  is,  when  its  geocentric  longitude  or  its  right  as- 
cension differs  180*  or  18^  f  rofa  that  of  the  sun.  At  such  a  time  tlie 
planet  will  rise  at  sunset  awi  culminate  at  midnight.  During  the 
t^ree  months  following  oppusition  the  planet  will  rise  from  three  to 
six  minutes  earlier  every  day,  so  tliat,  knowing  when  a  planet  is  in 
opposition,  it  is  easy  to  And  it  at  any  other  time.  For  example,  a 
month  after  opposition  the  planet  will  be  two  or  three  hours  Ugb 
about  sunset,  and  will  culminate,  about  nine  or  ten  o'clock.  Of 
course  the  inner  planeta  never  come  into  of^Kwition,  and  hence  an 
beat  seen  about  the  times  of  their  greatest  elon^pttlons. 


Dd  dbtance  of  the 
nd  heat  which  they 
•  eighty  time*  that 
t  and  beat  from  the 
Jiat  of  water,  while 

f  any  single  ptenet 
of  all  of  them.  In 
ny  given  planet  ex- 
:■■  maaa  than  itself, 
asses  of  tlie  planets 
ire  here  express  at 


1 

PbAMRa. 

1,000,000,000 

Mswes. 

imber,  is  unlinown, 
t  of  our  earth,  and 

masses  of  the  solar 
's  mass  is  thus  over 

the  fact  of  its  cen- 
Q  fact,  tlie  eentn  of 
lido  the  body- of  the 
turn  are  in  opposite 

about  the  sun  have 
lere  said  it  appears 

I  will  be  wlien  it  is 
ude  or  its  right  as- 
At  such  a  time  tlie 
night.    During  the 

II  rise  from  three  to 
when  a  planet  is  In 
e.  For  example,  a 
If  three  hours  Ugh 
t  ten  o'clock.  Of 
tion,  and  hence  an 
ilonai 


H! 


STRUCTURE  OF  THE  SOLAR  SYSTEM. 


190 


JMaeBsioBS  ef  the  Oolar  Vjrstem.— The  figure  gives  a  rough  plan  of 
part  of  the  solar  system  us  it  would  appear  to  a  spectator  immediately 
above  or  below  the  plane  of  the  ecliptic.  It  is  drawn  approximately 
to  scale,  the  mean  distance  of  the  earth  (=  1)  being  half  an  inch. 
The  mean  distance  of  Saturn  would  be  4-T7  inches,  of  Uranui  9-69 


T¥kVt. 


inches,  of  NeptHiu  IS '08  inches.    On  the  same  scale  the  distance  of 
the  neareri  fixed  star  would  be  108, 188  inches,  or  over  one  and  one  half 
miles. 
The  arrangement  of  the  planets  and  satellites  is,  then^-^ 


The  Inner  Group. 
Mercury. 
Venus. 

Earth  and  Moon. 
liars  and  2  moons. 


AateroMs. 

iMN)  minor  planets, 

and    probably 

pany  more. 


The  Outer  Oroop, 
I  Jupiter  and  4  moons. 
J  Saturn  and  8  moons. 
*]  Uranus  and  4  nuxms. 
(  Keptime  anj  1  moon. 


106 


A8TB0N0MT. 


To  avoid  rapetitioiu,  the  elements  of  the  ni»Jor  pltneta  anil  other 
data  are  collected  into  the  tvo  following  tablet,  to  which  reference 
■liuiild  be  made  hy  the  atuduiit.  The  unit*  io  term*  of  which  the  Tari- 
out  quantities  are  given  are  those  familiar  to  us,  as  miles,  days,  etc., 
yet  some  of  tlie  distances,  etc.,  are  so  immensely  greater  than  any 
known  to  our  daily  experience  that  we  must  have  recourse  to  illus- 
trations to  obtain  any  idea  of  tlicm  at  all.  For  example,  the  dis- 
tance of  the  SUB  is  said  to  tie  03i  mUliati  milef .  |t  Is  of  importance 
that  some  idea  should  be  |iad  of  this  distance,  as  it  is  the  tpiiit,  in 
terms  of  which  not  only  tiio  distances  in  tit*  solar  system  arc  ex- 
pressetl,  but  which  serves  as  a  basis  for  measures  in  the  stellar  uni- 
verse. Thus  when  we  say  that  tlie  distance  of  tlio  nearest  star  is  over 
200,000  times  tlie  mean  distance  of  tlie  pun,  it  becomes  necessary  to  see 
if  some  conception  can  be  obtained  of  one  factor  in  tliis.  Of  tlie  ab- 
stract number,  92,500,000,  we  )iave  no  conception.  It  is  far  too 
great  for  us  to  have  counted.  We  have  never  taken  in  at  one  view 
even  a  million  similar  discrete  objects.  The  largest  tree  has  less 
than  000,000  leaves.  To  count  from  1  to  200  requires,  with  very 
rapid  counting,  60  seconds.  Suppose  this  kept  up  for  a  day  wiiliout 
intermission  ;  at  the  end  we  should  have  counted  288.000,  which  is 
almul  ,^  of  88,000,000.  Hence  over  10  pnonlbs'  uninterrupli'<l 
counting  by  night  and  day  would  be  requireid  simply  to  enumerate 
the  number,  and  long  before  Mie  expiration  of  tlie  task  all  idea  of  it 
would  have  vanisiied  We  may  take  other  and  perhaps  more  atrik- 
ing  examples.  We  know,  for  instance,  that  the  time  of  the  fastest 
express  trains  between  Now  York  fiid  Chicago,  wliicb  avmige  40 
miles  per  hour,  is  about  a  day.  Buppoaa  sucti  a  train  to  Mart  for  the 
sun  and  to  continue  running  at  this  rapid  rate.  It  would  f»ke  888 
years  for  the  Journey.  Three  bupdreil  snd  si  vtylbm  yeus  ago  there 
was  not  a  European  settlement  in  America. 

A  canoon-bidl  moving  continuously  acraaa  tb«  intcnrenlag  apvce 
nt  its  highest  speed  would  require  about  nine  years  to  reach  the  sun. 
The  report  of  the  cannon,  if  it  could  be  convej'ed  to  the  sun  with 
the  velocity  of  sound  in  air,  would  arrive  there  five  years  after  the 
projectile.  Such  a  distance  is  entirely  inconcdvabU.  and  yet  it  ia 
only  a  small  fraction  of  th<jae  with  which  astronomy  has  to  deal,  eve^i 
in  our  own  system.    The  distance  of  Neptune  is  80  times  as  great. 

If  we  examine  the  dimensions  of  the  yarious  orba.  we  meet  ylnflat 
equally  inconceivable  numbers,  Tbe  diameter  of  the  svn  is  860,000 
miles;  its  radiua  is  but  480,000,  and  jet  this  is  nearly  twice  tlie  nean 
distance  of  the  moon  from  the  earth,  "fry  to  oopoeive,  la  looUiigat 
the  moon  In  a  clear  sky,  that  If  tfte  mintre  of  tlw  'W  Oo«ld  be  pliMid 

^  t)if  m^^  ^  tk«  mHIi.  tdo  nmM  vmld  bo  ivt  wltMn  (U8  wn'i 


*,.,«_ 


tlaneta  antl  otber 
wbich  reference 
at  which  the  Twi- 
inilee.  days,  etc., 
greater  than  any 
recourae  to  ilhis- 
txample,  the  din- 
It  of  importance 
it  it  the  i|iiit,  in 
ir  •jrtteni  arc  ex- 
n  the  stellar  iini- 
tareri  atar  is  over 
«  ueceaaary  to  lee 
this,  or  tlie  ab- 
I.  It  ia  far  too 
en  in  at  one  view 
:e«t  tree  h«ii  less 
liiirea,  with  very 
For  a  day  without 
288,000,  which  is 
la'  uninterrupti'd 
ply  to  enumerate 
tank  all  idea  of  it 
iiape  more  atrik- 
me  of  the  faatest 
liiich  armifc  40 
in  to  Mart  for  the 
would  t»ke  918 
w  yean  afo  there 

ntcrvenlnf  ap«ce 
to  reach  the  aim. 
to  the  sun  with 
e  years  after  the 
bU.  and  yet  it  ia 
'haatodflal,eTei)i 
limes  as  great. 
.  W0  meet  ylmsft 
be  sun  is  860,000 
y  twice  the  mean 
Ive.  In  looUnirtt 
I  could  be  p]«oi>il 
wltMn  tM  MW'i 


i 


8TRUCTURB  OF  THB  SOLAR  ST8TBM. 


\n 


I 


surface.  Or  again,  conceiTe  of  the  force  of  gravity  at  the  surface  of 
the  Tarious  bodies  of  the  system.  Al  the  sun  it  is  nearly  28  times 
that  known  to  us.  ▲  pendulum  beating  seconds  here  would,  if 
transported  to  the  sun.  vibrate  with  a  motion  more  rapid  than  that 
of  a  watob-balance.  The  muscles  of  the  strongest  man  would  not 
support  blm  erect  on  tb*  aurfaoe  oi  the  sun :  even  lying  down  be 
would  cruali  himself  to  death  under  hia  own  weight  of  two  tons. 
We  may  by  these  iUuatrations  get  some  rough  idea  of  the  meaning  of 
the  numbers  in  these  tables,  and  of  the  iacapabiiUy  of  our  Ihniled 
ideas  to  comprehend  the  true  dimensions  of  even  the  aukr  system. 


^SSm^j^ii:^.^^^--  ■  -.51 


198 


ASTRONOMY. 


1^  mt  vmrn'mmmmfeH^m'^'f*  ■Jiiw*»n«w^ 


e 


JO   t«    ^, 


US 


52    {2 


S9    9 


3®  s;  2 

22  f2  8 

Is  8  S   : 

SI)  9  9' 

no)  O  1-* 

DA  CO  00 


eco 


5 


IS  3 


»e» 


s   g 


.9 


« 

a    3   § 


I 


OQ 

3 


STRUCT VRB  OF  THE  SOLAR  aYSTBM. 


\m 


n 


i 


® 


s  s  s  s 

a     T^     00     ^ 
JH     ei     ^     1^ 


s  s  s  s 

OO       M       '<<•       « 


5^ 


S:    g    S    S    gS    $    S    2S 
P    9    S    8    8      Z    2    8"!" 


°-  Ik 


*   -3   -g 

S     ^     ^ 


»i     e«     40     e. 

© th       O       "-i 


$        S       OQ        S 


I 


o 


4)     *      .      . 

&  M  I 

&     &     U>     P 


§    S    S 


0t  9  00  *^ 

9  9  ■^  T* 

S  «  0)  04 

«  ■  t-'  t^  -^ 


s  g  s  af 


I 


TF 


S    S    S    ^    9      op 

M      10      »•      t^      ^  g 


O      O 


00       t> 

1-1 

o     o 


S    S    S    3    8      04 

e«     «     t^     t^     e»       jg 
g     e     e     e     o       e 


«o     t>     e 
58    e    ^ 


e     o 


8    8    8    8    8      % 

•H         1-«         1^         IH         f>4  IS 


.        44 


190 


3    8 


Ti 


CHAPTER  IL 


THE  BUH. 

OmoAi  IhwmMMt. 

To  enable  the  natare  of  the  phenomena  of  the  an  n  to  be 
dea/lj  nndenitood,  we  preface  oar  aoconnt  of  iti  phyiical 
conatitation  bj  a  brief  aanamary  of  iii  main  feataret. 

Pkotoiphere. — To  the  simple  Tieion  the  san  presents  the 
aspect  of  a  brilliant  sphere.  The  risible  shining  aurfact 
of  this  sphere  is  called  the  phofotphere,  to  distinguish  it 
from  the  body  of  the  sun  as  a  whole.  The  apparently  flat 
surface  presented  by  a  riew  of  the  photoiph«re  is  called  the 
snn's  di»k. 

ipAlA— When  the  photosphere  is  examined  with  a  tele- 
scope, small  dark  patches  of  taried  and  irregular  outline 
are  frw^uently  foiind  upon  it.  These  are  called  the  iolar 
tpoti. 

aetattea.-^Vhen  the  spots  era  obeei^ed  from  day  to 
day,  they  are  fonnd  to  moTeorer  the  snn's  disk  from  east  to 
west  in  soeh  a  way  as  to  show  that  the  snn  rotates  on  it« 
axis  in  a  period  of  26  or  29  days.  The  ran,  therefore,  has 
axi$,  poltt,  end  tquator,  like  the  earth,  the  axis  being  the 
line  Mound  which  it  roiatea. 

iMolai.— Oronpa  of  minute  apecka  brighter  than  the 
general  anrfaoe  of  the  aun  are  often  aeen  in  the  neighbor- 
hood  of  Bpota  or  ^where.    They  ar0  called /«<;«/<«. 


i  the  Ban  to  be 
ot  its  pbyiical 
ftfataret. 
in  presentg  the 
hining  aur/act 
distingnish  it 
apparently  flat 
ir«  is  called  the 

ed  wHh  a  tele- 
'egnktf  outline 
ailed  the  solar 

from  day  to 

sk  from  east  to 

rotates  on  its 

therefore,  has 

axis  being  the 

bter  than  the 
the  neighbor* 
i/acula. 


TBM  btllt. 


901 


Obromof^rt,  or  Sierra,— The  solar  photosphere  is  cot- 
ered  i.y  a  layer  of  glowing  vapors  and  gases  of  very  irregu- 
lar depth.  At  rhe  bottom  lie  the  rafon  of  Many  metals, 
iron,  etc.,  tsiatnised  hj  the  forvont  heat  which  reigns 
there,  while  the  upper  portions  are  oompcsed  principally 
of  hydrogen  gas.  This  vaporous  atmosphere  is  commonly 
called  the  ehromosp1m%  aoBMtimes  the  mstm.  It  ia«i- 
tirely  invisible  to  direct  vision,  whether  with  the  telescojie 
or  naked  eye,  except  for  a  few  seconds  about  the  beginning 
or  end  of  a  total  eclipse,  but  it  may  be  seen  on  any  clear 
day  through  the  spectroscope. 

Premiaeaeei^  Frotuheraaeea,  or  Sod  rhnofc— The  gases 
of  the  chromosphere  are  frequently  thrown  up  in  irregular 
masses  to  vast  heights  above  the  photosphere,  it  may  be 
60,000,  100,000,  or  even  300,000  kilometres.  Like  the 
chromosphere,  these  masses  have  to  be  studied  with  the 
spectroscope,  and  can  never  be  directly  seen  except  when 
the  sunlight  is  cut  off  by  the  intervention  of  the  moon 
during  a  total  eclipse.  They  are  then  seen  as  rose-colored 
flames,  or  pilot  of  bright  red  clouds  of  irregukr  and  fantas- 
tic shapes.  i 

Ooraaa.— During  total  eolipoes  the  sun  irseen  to  be  en- 
veloped by  •  mass  of  soft  white  light,  much  fainter  than 
the  ehromoophoro,  and  extending  out  on  sill  sidof  far  be- 
yond the  highest  prominences.  It  is  brightest  around  the 
edge  of  iho  tun,  and  fades  oft  toward  its  onter  boundary, 
by  insensible  gradations.  This  halo  of  light  is  called  the 
eoroM,  and  is  a  very  striking  object  during  a  total  eclipse. 


f4Ml*  Ml  IMMNM  sf  fM  ¥kHmilk$n.—thi  disk  6f  the  sna  is  d^ 
esflar  in  shiipe,  ntf  ttMter  #hiit  fide  of  tb«  ittn*s  gliAe  b  turned  tif- 


••'V.Hfjff^lf^. 


sod 


ASTRONOMY. 


ward  us,  whence  it  follows  that  the  sun  itself  is  a  sphere.  The  aspect 
of  the  disk,  when  viewed  witu  the  naked  eye,  or  with  a  telescope  of 
low  power,  is  that  of  a  UTiifortn  bright,  shining  surface,  hence  called 
the  photogpJiert.  With  a  telescope  of  higher  power  the  photosphere 
is  seen  to  be  dlTersified  with  groups  of  spots,  and  under  good  con> 


Fnk  IB.— KanovLATiD  AaaAiiaBinHT  or  tu  Sm'a 
Otom  a  photognnAu) 

ditions  the  whole  bums  has  a  mottled  or  curdled  appearance.  Thii 
mottling  is  caused  by  the  presence  of  cloud-like  forms,  whoM  out- 
lines though  faint  are  yet  distinguishable.  The  background  is  also 
covered  with  small  white  dots  or  forms  still  smaller  .than  tlks  c]ouda» 


here.  Theaapect 
itli  a  telescope  of 
face,  hence  called 
r  the  photosphere 
under  good  con> 


ipearance.  Thia 
rou,  whoM  out- 
digiound  ia  alto 
than  thjB  clouda» 


i 


THR  6UN. 


908 


These  are  the  "  rice-grains,"  so  called.  The  clouds  themseWes  are 
composed  of  small,  intensely  bright  bodies,  irregularly  distributed, 
of  tolerably  definite  shapes,  which  seem  to  be  suspended  in  or  super- 
posed  on  a  darlier  medium  or  background.  The  spaces  between  the 
bright  doU  vary  in  diameter  from  2'  to  4'  (about  1400  to  2800  kilo- 
metres). The  rice-grains  themselves  have  been  seen  to  be  composed 
of  smaller  granules,  sometimes  not  more  than  0'.8  (185  miles)  in 
diameter,  clustered  togetiicr.  Thus  there  have  been  seen  at  least 
three  orders  of  api^gation  in  the  brighter  parta  of  the  photosphere: 
the  larger  cloud-like  forms;  the  rice- grains;  and,  smallest  of  idl,  the 
granules. 

Light  and  Heat  from  the  Photoiphere. — The  photosphere 
is  not  equally  brig]  it  all  over  the  apparent  disk.  This  is  at 
once  evident  to  the  eye  in  observing  the  son  with  a  tele- 
scope. The  centre  of  the  disk  is  most  brilliant,  and  the 
edges  or  limbs  are  shaded  off  so  as  to  forcibly  suggest  the 
idea  of  an  absorptive  atmosphere,  which,  in  fact,  is  tl^e 
cause  of  this  appearance. 

Such  absorption  occurs  not  only  for  the  rays  by  which 
we  see  the  sun,  -the  so-called  visual  rays,  but  for  those 
which  have  the  most  powerful  effect  in  decomposing  the 
salts  of  silver,  the  so-called  chemical  rays,  by  which  the 
ordinary  photograph  is  taken. 

The  amount  of  heat  received  from  different  portions  of 
the  sun's  disk  is  also  variable,  according  to  the  part  of  the 
apparent  disk  examined.  This  is  what  we  shoald  expect. 
That  is,  if  the  intensity  of  any  one  of  these  radiations  (as 
felt  at  the  earth)  varies  from  centre  to  circomference,  that 
of  every  other  should  also  vary,  since  they  are  all  modifi- 
cations of  the  same  primitive  motion  of  the  sun's  con- 
stituent particles.  But  the  constitution  of  the  sun's  at- 
mosphere is  such  that  the  law  of  variation  for  the  three 
classes  is  different  The  intensity  of  the  radiation  in  the 
sun  itself  and  insido  of  the  absorptive  atmosphere  is  prob- 


1-  y*^ 


■JMIMMBBES 


Jjt!  '- 


ifn 


mi 


MTRONOMT. 


ably  nearly  constant.  The  ray  -vrbidi  leaves  the  centre 
of  the  sun's  disk  in  passing  to  the  earth  liaiiiiias  the 
smallest  possible  thickness  of  the  solar  atmosphere,  while 
the  rays  from  points  of  the  sun's  body  which  appear  to  us 
near  the  limbs  pass,  on  the  contrary,  through  the  maxi- 
mum thickness  of  atmosphere,  and  are  thus  longest  sub- 
jected to  its  absorptiye  action. 

This  is  plainly  a  rational  explanation,  since  the  part  of 
the  sun  which  is  seen  by  us  as  the  limb  varies  with  the 
position  of  the  earth  in  its  orbit  and  with  the  position  of 
the  sun's  surface  in  its  rotation,  and  has  itself  no  physical 
peculiarity.  The  various  absorptions  of  different  classes 
of  rays  correspond  to  this  supposition,  the  more  refrangi- 
'  ble  rays,  violet  and  blue,  suffering  most  absorption,  as  they 
must  do,  being  composed  of  waves  of  shorter  wave-length. 

Amount  of  Heat  Emitted  by  the  Sun.— Owing  to  the 
absorption  of  the  solar  atmosphere,  it  follows  that  we  re- 
ceive only  a  portion — perhaps  a  very  small  portion — of 
the  rays  emitted  by  the  sun's  photosphere. 

If  the  sun  had  no  absorptive  atmosphere,  it  would  seem 
to  us  hotter,  brighter,  and  more  blue  in  color. 

Exact  notions  as  to  how  great  this  absorption  is  are  hard 
to  gain,  but  it  may  be  said  roughly  that  the  best  authorities 
agree  that  although  it  is  quite  possible  that  the  sun's  at- 
mosphere absorbs  half  the  emitted  rays,  it  probably  does 
not  absorb  four  fifths  of  them. 

The  amount  of  this  absorption  is  a  practical  question  to 
us  on  the  earth.  So  long  as  the  central  body  of  the  san 
continues  to  emit  the  same  quantity  of  rays,  it  is  plain  that 
the  thickness  of  the  solar  atmosphere  determines  the  nnm- 
ber  of  wttoh  rays  reaching  the  earth.  If  in  former  timet 
this  atmosphere  was  much  thicker,  then  less  heat  would 


tei>iwii<Bw^arta^fci«rtiifiiiiWifi>i»j"iM^^^^^^  ".';«>'■■ 


eaves  the  centre 
"th  tnmnM  the 
itmosphere,  while 
hich  appear  to  us 
irough  the  maxi- 
shas  longest  sab- 

since  the  part  of 
b  varies  with  the 
h  the  position  of 
tself  no  physical 
different  classes 
e  more  refrangi- 
•sorption,  as  they 
ter  wave-length. 
— Owing  to  the 
Hows  that  we  re- 
mall  portion— of 

«,  it  would  seem 

Dior. 

'ption  is  are  hard 

e  best  authorities 

;hat  the  snn's  at- 

it  probably  does 

itical  question  to 
body  of  the  son 
rs,  it  is  plain  that 
rmines  the  anm- 
in  fonner  timM 
less  hc»t  would 


THS  SUIT. 


d06 


have  reached  the  earth.  Glacial  epochs  may  be  explained 
in  this  way.  If  the  central  body  of  the  sun  has  likewise 
had  different  emissive  powers  at  different  times,  this  again 
would  produce  a  variation  in  the  temperature  of  the  earth. 

Amount  of  Hest  Badikted. — There  is  at  present  no  wny  of  dctermin- 
ing  accurately  either  the  absolute  amount  of  heat  emitted  from  the 
central  body  or  the  amount  of  this  heat  stopped  by  the  solar  atmos- 
phere itself.  All  that  can  be  done  is  to  measure  (and  that  only 
roughly)  the  amount  of  heat  really  received  by  the  earth,  without 
attempting  to  define  accurately  the  circumstances  which  this  radiation 
has  undergone  before  reaching  the  earth. 

PomUiET  has  experimented  upon  this  question,  making  allowance 
for  the  time  that  the  sun  is  below  the  horizon  of  any  place,  and  for 
the  fact  that  the  solar  rays  do  not  in  general  strike  perpendicularly 
but  obliquely  upon  any  given  part  of  the  earth's  surface.  His  con- 
clusions may  be  stated  as  follows :  if  our  own  atmosphere  were  re- 
moved, the  solar  rays  would  have  energy  enough  to  melt  a  layer  of 
ioe  9  centimetres  thick  over  the  whole  earth  daay,  or  a  layer  of  about 
82  metres  thick  in  a  year. 

This  action  is  constantly  at  work  over  the  whole  of  the  sun's  sur- 
face. To  produce  a  similar  effect  by  the  combustion  of  coal  would 
require  that  a  layer  of  coal  5  metres  thick  spread  all  over  the  sun 
Should  be  consumed  every  hour.  This  is  equivalent  to  a  eontinuotu 
evolution  of  10,000  horse-power  on  every  square  foot  of  the  sun'i 
surface.  If  the  sun  were  of  solid  coal  and  produced  its  own  heat  by 
combustion,  it  would  bum  out  in  6000  years. 

Of  this  enormous  outflow  of  heat  the  earth  receives  only 
nvnbnw  ^*  *'*'®  expressed  the  power  of  even  this  small  frac- 
Uoiifof  ihe  sun's  heal  in  terms  of  the  ice  it  would  melt  daily.  If  we 
compute  how  much  coal  it  would  require  to  melt  the  same  amount, 
and  then  further  calculate  how  much  work  this  coal  would  do,  we 
Shan  find  that  the  sun  sends  to  the  earth  an  amount  of  heat  which  is 
equivalent  to  one  horse-power  continuously  acting  for  every  80 
square  feet  of  the  earth's  surface.  Most  of  this  is  expended  in  main- 
taining the  earth's  temperature;  but  a  small  portion,  about  -i^,  is 
stored  away  by  animals  and  vegetables,  and  this  slight  fraction  it 
the  souroe  upon  which  the  human  race  depends.  If  this  were  with- 
drawn the  race  would  perish. 

Of  the  total  amount  of  lient  rndiated  by  the  sun  the  earth  receives 
6at  an  imfgniflcnnt  share.  The  ruii  is  capable  of  heating  the  oitlre 
•urface  of  a  sphere  whose  rnilius  is  the  earth's  mean  distance  t6  the 


■I.: 


V' 


d06 


A8TR0N0MT. 


nine  degree  that  the  earth  is  now  heated.  The  surface  of  such  a 
sphere  Is  2,170,000,000  times  greater  than  tlie  angular  dimensions  of 
the  earth  as  seen  from  tlic  sun,  and  licnce  the  earth  receives  less  than 
one  two-billioDth  part  of  tlie  soliir  radiation.  The  rest  of  the  solar 
rays  are,  so  far  as  we  know,  lost  in  space. 

lelar  Temperature.— From  tiic  amount  of  heat  actually  radiated  by 
the  sun,  attempts  liave  been  made  to  determine  the  actual  tempera- 
ture of  tiie  solar  surface.  The  estimates  reached  by  various  authori- 
ties differ  widely,  as  the  laws  which  govern  the  absorption  within 
the  solar  cnvelopo  are  almost  unknown.  Some  such  law  of  absorp- 
tion has  to  be  supposed  in  any  such  investigation,  and  the  estimates 
have  differed  widely  according  to  the  adapted  law. 

Skcchi  estimates  this  temperature  at  about  6,100,000°  C.  Other 
estimates  are  far  lower,  but,  according  to  nil  sound  pliilosophy,  the 
temperature  must  fur  exceed  any  terrestrial  temperature.  There  can 
be  no  doubt  that  if  the  temperature  of  the  earth's  surface  were  sud- 
denly raised  to  that  of  the  sun,  no  single  chemical  element  would  re- 
main in  its  present  condition.  The  most  refractory  materials  would 
be  at  once  volatilized. 

We  may  concentrate  the  heat  received  upon  several  square  feet 
(the  surface  of  a  huge  burning-lens  or  mirror,  for  instance),  examine 
its  effects  at  the  focus,  and,  making  allowance  for  the  condensation 
by  the  lens,  see  what  is  the  minimum  possible  temperature  of  the 
•un.  The  temperature  at  the  focus  of  the  lens  cannot  be  higher  than 
that  of  the  source  of  heat  in  the  sun ;  we  can  only  concentrate  the 
heat  received  on  the  surface  of  the  lens  to  one  point  and  examine  its 
effects.  If  a  lens  three  feet  in  diameter  be  used,  the  most  refractory 
materials,  aa  fire-clay,  platinum,  the  diamond,  are  at  once  melted  or 
▼olatilized.  The  effect  of  the  lens  is  plainly  the  same  as  if  the  earth 
were  brought  closer  to  llie  sun.  in  the  ratio  of  the  diameter  of  the 
focal  image  to  that  of  the  lens.  In  the  case  of  the  ku'  of  three  feet, 
allowing  for  the  absorption,  etc..  this  distance  is  yet  greater  than 
that  of  the  moon  from  the  earth,  so  that  it  appears  that  any  comet  or 
planet  so  close  as  this  to  the  sun,  if  composed  of  materials  similar  to 
those  in  the  earth,  must  be  vaporized. 


UiHt^ 


BW-fPOn  ASB  Faodxjil 

A  very  cursory  examination  of  the  sun's  disk  with  a  small  tcle- 
■cope  will  generally  abow  one  or  more  dark  spots  upon  the, photo- 
■friiere.  These  are  of  various  sizes,  from  minute  black  dots  1'  of  3' 
in  dhuneter  (1000  kilometres  or  less)  to  large  spoto  several  minutes 
of  are  in  extent 


fi^n'^'-^'  '-^^■^■•*'"^ 


'ho  surface  of  such  a 
ngulnr  diiiiciisious  of 
irth  receives  less  than 
riie  rest  of  the  solar 

;  actually  radiated  by 
I  the  actual  temperu- 
d  by  various  authori- 
lie  absorption  vithiu 
I  such  law  of  absorp- 
>n,  and  the  estimates 
aw. 

e.lOO.OOO'  C.  Other 
)uud  philosophy,  the 
ipcraturo.  There  can 
h's  surface  were  sud- 
cal  element  would  re- 
:tory  materials  would 

n  several  square  feet 
for  instaucc),  examine 
for  the  condensation 
e  tcmperuturo  of  the 
cannot  be  higher  than 
only  concentrate  the 
point  and  examine  its 
1,  the  most  refractory 
are  at  once  melted  or 
«  same  as  if  the  earth 
)f  the  diameter  of  the 
theleii'  of  three  feet, 
e  is  yet  greater  than 
ears  that  any  comet  or 
of  materials  similar  to 


isk  with  a  small  tcle- 
ipots  upon  the.piioto* 
lite  blaciL  dots  1' Of  2' 
spots  several  minutes 


THE  8UN. 


207 


Solar  spots  generally  have  a  dark  central  nu<ku$  or  vmbra,  sur- 
rounded by  a  border  or  penumbra  of  grayish  tint,  intermediate  in 
shade  between  the  central  blackness  and  the  bright  photosphere. 
By  increasing  the  power  of  the  telescope,  the  spots  are  seen  to  be  of 
very  complex  forms.  The  umbra  is  often  extremely  irregular  in 
shape,  and  is  sometimes  crossed  by  bridges  or  ligamenU  of  shining 
matter.  Tlie  penumbra  is  composed  of  filaments  of  brighter  and 
darker  light,  wliich  are  arranged  in  slrite.  Tlie  general  aspect  of  a 
spot  under  considerable  magnifying  power  is  shown  in  Pig.  59. 

The  first  printed  account  of  solar  spots  was  given  by  Fabbittos  in 
1811,  and  Oaulko  ift  tlie  same  year  (May,  1611)  also  described  them. 


FlO.  M.— VMHU  AMD  PBTOItBRA  OF  BOM-aPOT. 


OAi.iLieo'8  observations  showed  them  to  belong  to  the  sun  itself,  and 
to  move  uniformly  across  tlie  solar  disk  from  east  to  west.  A  spot 
Just  visible  at  the  east  limb  of  the  sun  on  any  one  day  travelled  slow- 
ly across  the  disk  for  12  or  14  days,  when  it  reached  the  west  Umb, 
behind  which  it  disappeared.  After  about  the  same  period,  it  reap- 
pears at  the  eastern  limb,  unless,  as  is  often  the  case,  it  has  in  the 
mean  time  vanished. 

The  spots  are  not  permanent  in  their  nature,  but  are  formed  some- 
where  on  the  sun,  and  disappear  after  lasting  a  few  days,  weeks,  or 
months.  But  so  long  as  they  last  they  move  regularly  from  east  to 
wwt  on  the  sun's  apparent  disk,  making  one  complete  rotation  ii) 


.1   \l 


;.  1 

1  J 


.-,mmmmmmm 


'mmm..^ 


306 


ASTROXomr. 


about  95  days.    This  period  of  2S  days  is  therefore  approximately 
the  rotation  period  of  the  snn  itself. 

■petted  Beftea.— It  is  found  that  the  spoU  are  chiefly  confined  to 
two  zonea,  one  in  each  hemisphere,  extending  from  nbout  10°  to  85" 
or  40°  of  lieliograph^c  latitude.  In  tlie  polar  region  spots  are 
scarcely  ever  seen,  and  on  the  solar  equator  tliey  arc  much  more  rare 
than  in  latitudes  10°  north  or  south.  Connected  witli  tlie  spots,  but 
lying  on  or  above  the  solar  surface,  are  faeulm,  mottliugs  of  light 
brighter  than  the  general  surface  of  the  sun. 


\    ? 


Ita.  flO.— FmnMBtfB  or  tbb  Smr. 


Mar  Axis  and  Iqnater.— The  spots  must  revolve  with  the  surface 
of  the  sun  about  his  axis,  and  tiie  directions  of  tlieir  motions  must  be 
approximately  parallel  to  his  equator.  Fig.  61  shows  the  appear- 
auoes  as  actually  observed,  the  dotted  lines  repreeenting  the  apparent 
paths  of  the  spoU  across  the  sun's  disk  at  different  times  of  the  year. 
In  June  and  Decemlier  these  paths,  to  an  observer  on  the  earth,  secsn 
to  be  right  lines,  and  hence  at  these  times  the  observer  mqst  be  in  the 
plane  of  the  solar  equator.  At  other  times  the  paths  are  ellipses,  and 
in  March  and  September  the  planes  of  these  ellipses  are  most  oblique, 

Swing  the  spectator  to  be  then  furthest  from  the  plane  of  tlie  solar 
ator.    The  inclination  of  the  solar  equator  to  the  ecliptic  is  about 
T  9',  HM  Mt«  «Xi*  of  V>^V>»  i*  o(  course  perpendi^qlKr  to  it. 


fore  •pproxinmtely 

chiefly  confined  to 
>ni  about  10°  to  SS' 
■  region  ipota  «re 
arc  much  more  rare 
witli  tlie  apols,  but 

mottliugB  of  iig^t 


live  with  the  surfaoe 
leir  motiona  must  be 
i  shows  the  appear- 
lenting  the  apparent 
at  times  of  the  year. 
>r  on  the  earth,  seem 
lerver  mqst  be  in  the 
kths  are  ellipses,  and 
ses  are  most  oblique, 
be  plane  of  the  solar 
the  ecliptic  is  abotit 
di^qhtr  to  it. 


me" 


ill 


THB  8Uy. 


900 


Vatiir*  of  til*  Spott.— The  sun-spota  are  really  depres 
■ions  in  the  photosphere,  as  was  first  pointed  out  by  Ax- 
DRBW  Wilson  of  Glasgow  in  1774.    When  a  spot  is  seen  at 
the  edge  of  the  diik,  it  appears  as  a  notch  in  the  limb,  and  is 


FM.  M.— AfTAMnr  Path  or  Solar  Spot  at  DimasKT  SsAaoHS. 

dliptioal  in  shape.    As  the  rotation  carries  it  farther  and 
farther  on  to  the  disk,  it  becomes  more  and  more  nearly 
oirci'lar  in  shape,  and  aftor  passing  the  centre  of  the  disk , 
the  i^pearanoes  take  place  in  reverse  order. 

These  obaerratioiis  were  ex|dained  by  Wilsoh,  and  more  fully  bj 
Sir  WnutM  ffwicwp..  b^  suppoeinK  t)M  w^  to  coaslrt  9f  aa  fah 


310 


ABTRONOMT. 


terior  dark  cool  mMi,  surrounded  by  two  layers  of  clouds.  The 
outer  layer,  which  forma  the  risible  pbotosplicre,  waa  supposed  ex- 
tremely brilliant.  Tlie  inuer  layer,  which  could  not  be  seen  except 
when  a  cavity  existed  in  the  photosphere,  was  supposed  to  lie  dark. 
The  appearance  of  the  edges  of  a  spot,  which  has  been  duscrihed  as 
the  penumbra,  waa  supposed  to  arise  from  tliose  dark  clouds.  Tiie 
spots  themselves  are,  according  to  this  view,  nothing  but  openings 
through  both  of  the  atmospheres,  tiie  nueletu  of  the  spot  being  simply 
the  black  surface  of  the  inner  sphere  of  the  sun  itself. 
Ttaia  theory.  Fig.  02,  accounu  for  the  facta  aa  they  were  knoi^n 


n*.  aa.— ArPCAaAMOc  or  a  Stct  xbab  nm  Lma  a»d  imAB  ibb 
Caaraa  or  thb  Sini. 


to  HsRSOBaL.  But  when  it  is  confronted  with  the  questions  of  the 
cause  of  tlie  sun's  heat  and  of  the  method  by  which  this  heat  haa 
been  maintained  constant  in  amount  for  centuries,  it  breaks  down 
completely.  The  conclusions  of  Wilsoh  and  Hbrschbl,  that  the 
spots  are  depressions  in  the  sun's  surface,  are  undoubted.  But  the 
existence  of  a  cool  central  and  solid  nucleus  to  the  sun  is  now 
known  to  be  impoasible.  The  apparently  black  centres  of  the  spota 
are  so  mostly  by  contrast  If  they  were  seen  against  a  perfectly 
black  background,  they  would  appear  very  bright,  as  haa  been 
proTed  b^  photometric  menauren.    ^nd  a  cool  solid  naclem  li«nfatl| 


IrtntfittWitiwarmnK 


rs  of  clouds.    The 
I,  waa  Biippoaed  ex- 

not  be  seen  except 
ipposed  to  bo  (hirk. 
8  been  described  ub 

dark  clouds.    The 
tiling  but  opeuinga 
le  spot  being  simply 
self, 
I  they  were  known 


i 


AMDimiBTBB 

;h0  questions  of  the 
irhich  this  heat  hu 
les,  it  breaks  down 
Ibrschbl,  that  the 
Ddoubted.  But  the 
to  the  sun  is  now 
centres  of  the  spots 
against  a  perfectly 
right,  as  has  been 
lUd  nacleiis  )i«n^tl| 


TBE  BUN. 


911 


such  an  atmosphere  as  HEiiscnKi.  sup^  iA  would  soon  become  gas- 
eous by  the  conduction  and  radiation  of  the  heat  of  the  photosphere. 
The  supply  of  solar  heat,  which  has  been  very  nearly  constant  dur- 
ing the  liistoric  period,  in  a  sun  so  constituted  would  haye  sensibly 
diminished  in  a  few  hundred  years.  For  ihese  and  other  reasons 
the  hypothesis  of  Hkrscbbl  must  be  modified,  sare  as  to  the  fact 
that  the  spots  are  really  cavities  in  the  photosphere. 

Hnmber  and  Periodieity  of  Solar  Spots. — The  number  of 
Bolar  spots  which  come  into  view  raries  from  year  to  year. 
Although  at  first  sight  this  might  seem  to  be  what  we  call 
a  purely  accidental  circumstance,  like  the  occurrence  of 
cloudy  and  clear  years  on  the  earth,  observations  of  sun- 
spots  establish  the  fact  that  this  number  xatiea  periodically. 

The  periodicity  of  the  spots  will  appear  from  the  following  sum- 
mary: 

From  1828  to  1881  the  sun  was  without  spots  f>n  only     1  day. 


In  1888 

From  1888  to  1840 

In  1848 

From  1847  to  1851 

In  1808 

From  18S8  to  1881 

In  1887 


ISVdaya. 

8  " 
147  " 

3  " 
198  •• 
no  day. 
195  days. 


Every  11  years  there  is  a  minimum  number  of  spots,  and  about  5 
years  after  each  minimum  there  is  a  maximum.  If,  instead  of  mere- 
ly counting  the  number  of  spots,  measurements  are  made  on  solar 
photographs  of  the  extent  of  tpotUdarea,  the  period  comes  out  with 
greater  distinctness.  This  periodicity  of  the  area  of  the  solar  spots 
appears  to  be  connected  with  magnetic  phenomena  on  the  earth's 
surface,  and  with  the  number  of  auroras  visible.  It  has  been  sup- 
posed to  be  connected  also  with  variations  of  temperature,  of  rain- 
fall, and  with  other  meteorological  phenomena  such  as  the  monsoons 
of  the  Indhm  Ocean,  etc.  Tlio  cause  of  this  periodicity  is  as  yet  un- 
known. It  probably  lies  within  the  sun  itself,  and  is  similar  to  the 
cause  of  the  periodic  action  of  a  geyser.  As  the  periodic  variations 
of  the  spots  correspond  to  variations  of  the  magnetic  needle  on  the 
earth,  it  appear*  that  there  in  a  connection  of  an  unknown  natuis 
between  the  sun  and  the  earth. 


212 


ABTRONOMT. 


\  , 


% 


t      ': 


TBI  Sxnr'i  CnoMosPHixK  avb  Coioita. 

nraomraa  of  Tot»l  leUpm.— The  Ijcgiiinlng  of  n  total  iolor 
eclipse  is  marked  simply  by  llio  small  black  notch  made  in  the 
luminous  disk  of  the  sun  by  the  advancing  edge  or  limb  of  the 
moon.  Tills  always  occurs  on  the  western  half  of  the  sun,  as  the 
moon  moves  from  west  to  cast  In  lis  orbit.  An  hour  or  more  must 
elapse  before  ihe  moon  has  advanced  sufficiently  far  in  its  orbit  to 
cover  the  sun's  disk.  During  this  time  the  disk  of  the  sun  is  gradu- 
ally hidden  until  it  becomes  a  thin  crescent. 

The  actual  amount  of  the  sun's  light  may  bo  diminished  to  two 
thirds  or  three  fourths  of  Its  ordinary  amount  without  its  Ixjlng 
•trlkinfrly  perceptible  to  the  eye.  What  is  first  noticed  is  the  change 
which  takes  place  in  the  color  of  the  surrounding  landscape,  which 
begins  to  wear  a  ruddy  aspect.  This  grows  more  and  ir.ore  pro. 
nounced,  and  gives  to  the  adjacent  country  that  weird  effect  which 
lends  so  much  to  tin  impresslveness  of  a  total  eclipse.  The  reawm 
for  the  change  of  color  is  simple.  We  have  already  said  that  the 
Bun'a  atmosphere  aUo:bs  a  large  proportion  of  the  bluer  rays,  and  aa 
this  absorption  Is  dcTiendcnt  on  the  thickness  of  the  solar  atmosphere 
through  which  the  rays  must  pass,  it. Is  plain  that  Just  before  tlio  sun 
is  totally  covered  the  rays  by  which  we  sec  it  will  be  redder  than 
ordinary  sunlight,  as  they  are  those  which  come  from  points  near 
the  sun's  limb,  where  they  have  to  pasa  through  the  greateat  thick- 
ness of  the  sun's  atmosphere. 

The  color  of  the  light  becomes  more  and  more  lurid  up  to  the  mo- 
m-iXki  when  the  sun  has  nearly  disappeared.  If  the  spectetor  is  upon 
th  1  ?np  of  a  high  mountain,  he  can  then  begin  to  see  the  moon's 
■hrdow  rushing  toward  him  at  the  rate  of  a  kilometre  in  about  a 
aecond.  Jtist  as  thp  shadow  reaches  him  there  ifc  a  sudden  increase 
of  darkness;  the  brighter  atars  begin  to  shine  in  ^e  darli  lurid  sky, 
the  thin  crescent  of  the  sun  breaks  up  into  small  points  at  dote  of 
lijrht,  which  suddenly  disappear,  and  the  moon  itself,  an  intensely 
black  ball,  appears  to  hung  isolated  in  the  heavens. 

An  insUint  afterward  the  corona  is  ^:een  surrounding  thfi  black 
di!>k  of  the  moon  with  a  soft  effulgence  quite  different  from  any 
other  light  known  to  us.  Near  Ihe  moon's  limb  It  is  intensely  bright, 
and  to  the  naked  eye  uniform  in  structure;  V  or  IC  from  the  limb 
this  Inner  corona  has  a  boundary  more  or  less  deflned.and  from  this 
extend  streamers  and  wlng8  of  fainter  and  more  nebnioaa  light 
These  are  of  variona  shapes,  sizes,  and  brilliancy.  No  two  aolw 
^paea  ^et  qbsepre^  hay^  been  ^\\}ffi  in  tUia  respect, 


It 


THE  SUN. 


21B 


DBOVA. 

of  K  total  folar 
)tch  made  in  the 
;e  or  limb  of  the 
of  the  8UD,  ns  the 
)ur  or  more  must 
far  in  its  orbit  to 
!  the  sun  is  gradu- 

liminislicd  to  two 
witliout  its  Iwing 
ticcd  is  llie  change 
landscape,  wliich 
ire  and  iriore  pro. 
vcird  effect  which 
ipse.  The  reason 
iady  said  that  the 
bluer  rays,  and  u 
B  solar  atmosphere 
just  before  the  sun 
rill  be  redder  than 
from  points  near 
the  greatest  thick- 

urid  up  to  the  mo- 
9  spectator  is  upon 
to  see  the  moon's 
smetre  in  about  a 
a  sudden  increase 
le  darli  lurid  sky, 
points  or  dots  of 
Itself,  an  intensely 
s. 

)iinding  thn  black 
llfferent  from  any 
is  intensely  bright, 
W  from  tlif  limb 
ned.and  from  this 
re  nebulous  light 
;y.    No  two  eoUHr 


These  appearances,  though  clinngpable,  do  not  change 
the  moon's  shadow  requires  to  pass  from  Vancouver's  Island  to 
Texas,  for  example,  which  is  some  fifty  minutes. 

Superposed  upon  tliese  wings  may  lie  seen  (sometimes  with  the 
naked  eye)  tiie  red  flames  or  protulierances  which  were  flrst  discov- 
ered during  a  solnr  eclipse.  These  need  not  be  more  closely  de- 
scribed here,  OS  they  can  now  be  studied  at  any  time  by  aid  of  the 
spectroscope. 

The  total  phase  lasts  for  a  few  minutes  (never  more  than  six  or 
sevenX  «>d  during  tliis  time,  as  tiie  eye  becomes  more  and  more 
accustomed  lo  the  faint  light,  the  outer  corona  is  seen  to  stretch 
further  and  further  away  from  the  sun's  limb.  At  the  erllpso  of  1878, 
July  20th,  it  was  seen  to  extend  more  than  6°  (about  9,000,000  miles) 
from  the  sun's  limb.  Just  before  the  end  of  the  total  phase  there  it 
a  sudden  increase  of  the  brightness  of  the  sky,  due  to  the  increased 
illumination  of  the  earth's  atmosphere  near  the  observer,  and  in  a 
moment  more  the  sun's  rays  are  agnin  visible,  seemingly  as  briglit  as 
ever.  From  the  end  of  totality  till  tlie  last  contact  tha  phenomena 
of  the  flrst  half  of  the  eclipse  are  repeated  in  inverse  order. 

Telaseopie  Aapeet  «f  the  Oereaa.— Sudi  are  the  appearances  to  the 
naked  eye.  The  corona,  as  seen  through  a  telescope,  is,  however, 
of  a  very  compUoated  structure.  The  inner  corona  is  usually  com- 
posed of  bright  strisB  or  fllaments  separated  by  darker  bonds,  and 
some  of  these  latter  are  sometimes  seen  to  lie  almost  totally  black. 
The  appearances  are  extremely  irregular,  but  they  are  often  as  if  the 
inner  corona  were  made  u|t  of  brushes  of  light  on  a  darker  back- 
ground. 

The  corona  and  red  prominences  are  sohtr  appendages.  It  was 
formerly  doubtful  whether  the  corona  was  an  atmosphere  belonging 
to  the  sun  or  to  the  m»n.  At  the  eclipse  of  1860  it  was  proved  by 
measurements  that  the  red  prominences  belonged  to  the  sun  and  not 
to  the  moon,  since  the  moon  gradually  covered  them  by  its  motion, 
they  remaining  attached  to  the  sun.  The  corona  has  also  since  bivn 
shown  to  lie  a  solar  appendage. 

Oasaeas  Vatwe  ef  the  Prealawees.— The  eclipse  of  1868  (July) 
was  total  in  India,  and  was  observed  by  many  skilled  astronomers. 
A  discovery  of  M.  JAifSSBN's  will  make  this  eclipse  forever  memora- 
ble. He  was  providc«l  with  a  spectroscope,  and  by  It  observed  the 
prominences.  One  prominence  in  particular  was  of  vast  size,  and 
when  the  spectroscope  was  turned  upon  it,  its  spectrum  was  discon* 
tinuone,  showing  the  bright  lines  of  hydrogen  gas. 

The  brightness  of  the  spectrum  was  so  marked  that  JAnanni  deter. 
miB#d  to  keep  his  spectroccope  dsed  upon  it  even  after  the  rcappear> 


-SBW 


I  Jje 


di4 


ASTRONOMr. 


ri«.  •S.-Svu'i  QoKoaA  PVBiM  nu  Ecum  ov  Jolt  M,  Itn, 


Am*'        ■ 


t  Swt  M,  1SI9. 


m^».imj"^m 


it 


TBK  8VK. 


^ib 


fence  of  (unliglit,  to  lee  hoir  long  It  could  be  followed.  It  wrh  found 
that  Us  ■pectruin  could  ittill  be  seen  ufter  the  return  of  complete  lun- 
linht;  and  not  only  on  that  day,  but  on  Kubaequent  dayi,  ainilhir 
phenoniuna  could  be  obaerved. 

One  great  diftlculty  wait  conquered  in  an  Inttant.  The  red  flames 
which  formerly  were  only  to  be  seen  for  a  few  moments  during  the 
comparatively  ruro  occurrences  of  total  eclipses,  and  whose  obserra- 
tion  demanded  long  and  expensive  Journeys  to  distant  parts  of  the 
world,  could  now  be  regularly  observed  with  all  the  facilities  offered 
by  a  fixed  observatory. 

This  great  step  In  advance  was  independently  made  by  Mr.  Locx- 


Tm.  64.— Vowa  or  tsi  Soua  Paoimnnoia  as  i 


TSR,  and  his  discovery  was  derived  from  pure  theory,  unaided  by  the 
eclipse  itself.  By  this  method  the  prominences  have  been  carefully 
mapped  day  by  day  all  around  the  sun,  and  it  has  been  proved  that 
around  this  body  there  is  a  vast  atmosphere  of  hydrogen  gas— the 
ehnmo^then  or  aierra.  From  out  of  this  the  prominences  are  pro- 
jected sometimes  to  heights  of  100,000  kilometres  or  more. 

It  will  be  necessary  to  recall  the  miln  facts  of  observation  which 
are  fundamental  in  the  use  of  the  sjMctroKOope.  When  a  brilliant 
point  is  examined  with  the  spectroscojjii;,  it  is  spread  out  by  the  prism 
into  a  band— the  spectrum.  Using  two  prisms,  the  spectrum  be* 
longer,  but  the  light  of  the  surface,  being  spiMQ  over  a 


216 


AaiRONOMT. 


Ill 


greater  area,  is  enfeebled.  Three,  four,  or  mora  prisms  spread  out 
the  spectrum  proportionally  more.  If  the  spectrum  is  of  an  incan- 
descent solid  or  liquid,  it  is  always  continuous,  and  it  can  l)e  en- 
feebled to  any  degree;  so  that  any  part  of  it  can  be  made  as  feeble  as 
desired. 

This  method  is  precisely  similar  in  principle  to  the  use  of  the  tele- 
scope in  viewing  stars  in  the  daytime.  The  telescope  lessens  the 
brilliancy  of  the  sky,  while  the  disk  of  the  star  is  kept  of  the  same 
intensity,  as  it  is  a  point  in  itself.  It  thus  becomes  visible.  The 
spectrum  of  a  glowing  gas  will  consist  of  a  definite  number  of  lines, 
say  three— A,  B,  C.  for  example.  Now  suppose  the  spectrum  of  this 
gas  to  be  superposed  on  the  continuous  spectrum  of  the  sun;  by 
using  only  one  prism,  the  solar  spectrum  is  short  and  brilliant,  and 
every  part  of  it  may  be  more  brilliant  than  the  line  spectrum  of  the  gas. 
By  increasing  the  dispersion  (the  number  of  prisms),  the  solar  spec- 
trum is  proportionately  enfeebled.  If  the  ratio  of  the  light  of  the 
bodies  themselves,  the  sun  and  the  gas,  is  not  too  great,  the  continu- 
ous spectrum  may  lie  so  enfecbletl  that  the  line  spectrum  will  be 
visible  when  superposed  upon  it,  and  the  spectrum  of  the  gas  may 
tlien  be  seen  even  in  the  prvsence  of  true  sunlight.  Such  was  the 
process  imnginod  and  successfully  carried  out  by  Mr.  Lockyer,  and 
such  is  in  essence  the  method  of  vivwing  the  promiuences  to-day 
adopted 

r  Tki  Gnroaal  IpMtnw.— In  1860  (August  7th)  a  total  solar  eclipse 
was  visible  in  the  United  Stales.  It  was  probably  observed  by  more 
astronomers  than  any  prece<ling  eclipse.  Two  Americim  astron- 
omers. Professor  YocMo,  of  Durimouih  College,  and  Professor  Habk- 
KKsa,  of  the  Svit\  Observatory,  csiwcially  observed  the  spectrum  of 
the  corona.  This  spectrum  was  found  to  consist  of  one  faint  green- 
ish lino  crossing  a  faint  continuous  spectrum.  The  place  of  this  line 
in  the  maps  of  the  solar  spectrum  published  by  KiBCHHorF  was  oc- 
cupied by  a  line  which  he  had  attributed  to  tlie  iron  spectrum,  and 
which  hnd  been  numbered  1474  in  his  list,  so  that  it  is  now  spoken 
of  as  1474  K.  This  line  is  probably  due  to  some  gas  which  must  be 
present  in  large  and  possibly  variable  quantities  in  the  corona,  and 
which  is  not  known  to  us  on  the  earth,  in  this  form  at  least.  It  is 
probably  a  gas  even  lighter  than  hydrogen,  as  the  existence  of  this 
line  has  been  traced  W  or  20'  from  the  sun's  limb  nearly  all  around 
the  disk. 

In  the  eclipse  of  July  89th.  1878,  which  was  total  in  Culoiado  and 
Texas,  the  continuous  spectrum  of  the  corona  was  found  to  be 
crossed  by  the  dark  lines  of  the  solar  spectrum,  showing  that  tte 
coronal  li^ht  was  compoacd  in  part  of  reflected  8unU|^ 


TBB  8uy. 


217 


m 


prisms  spread  out 
im  is  of  an  incan- 
tnd  it  can  be  en- 
I  made  aa  feeble  as 

the  use  of  the  tele- 
sscope  lessens  the 
I  kept  of  the  same 
tmes  visible.  The 
B  number  of  lines, 
le  spectrum  of  this 
m  of  the  sun;  by 
and  brilliant,  and 
)ectrumof  the  gas. 
as),  the  solar  spec- 
f  the  light  of  the 
;reat,  the  continu- 
spectrum  will  be 
m  of  the  gns  may 
lit.  Such  was  the 
Mr.  LocKYER,  and 
'omincncea  to-dny 

total  sulnr  eclipse 
observed  by  more 
American  aslron- 
i  Professor  Habk- 
il  the  spectrum  of 
if  one  faint  green- 
9  place  of  this  line 
iBCHHorF  was  00- 
•on  spectrum,  and 
t  it  is  now  spoken 
;tM  which  must  be 
1  the  corona,  and 
rm  at  least.  It  is 
I  existence  of  this 
nearly  all  around 

1  in  Culoiado  and 
was  found  to  be 
showing  that  Um 


fiovkOEt  or  tax  Snr's  Heat. 

Theoriei  of  the  Sun's  Conrtitation. — No  considerable 
fraction  of  the  heat  rudiuted  from  the  snn  returns  to  it 
from  the  celestial  Bjacod.  But  we  know  the  sun  is  dully 
radiating  into  space  2,170,000,000  limes  as  much  heat  as 
is  daily  received  by  the  earth,  and  it  follows  that  unless 
the  supply  of  heat  is  infinite  (which  we  cannot  believe)  this 
enormous  daily  radiation  must  in  time  exhaust  the  supply. 
When  the  supply  is  exhausted,  or  even  seriously  trenched 
upon,  the  result  to  the  inhabitants  of  the  earth  will  be  fatal. 
A  slow  diminution  of  the  daily  su|)ply  of  heat  wonld  pro- 
duce a  slow  change  of  climates  from  hotter  toward  colder. 
The  serious  results  of  a  full  of  50°  in  the  mean  annual  tem- 
perature of  the  earth  will  be  evident  when  we  remember 
that  such  a  fall  would  change  the  climate  of  France  to  that 
of  Spitzbergen.  The  temi>crutnre  of  the  sun  cannot  be 
kept  up  by  the  mere  combustion  of  its  materials.  If  the 
sun  were  solid  carbon,  and  if  a  constant  and  adequate  supply 
of  oxygen  were  also  present,  it  has  been  shown  that,  at  the 
present  rate  of  radiation,  the  heat  arising  from  the  com- 
bustion of  the  mass  would  not  last  more  thau  6000  years. 

An  explnnntion  of  the  solnr  heat  and  light  has  tieen  sufrgestfd, 
which  (lepciids  u|M>n  the  fact  tliut  great  imiouiils  of  lieiit  ami  light 
are  procluftKi  by  the  ollision  uf  two. rnpiUly  moving  lipuvy  iNulies, 
or  even  by  the  pasmge  nf  a  heavy  lto*l>  like  a  mctiorile  tlirougb  Die 
earth's  atmosphere.  In  fact,  if  wc  had  a  certain  mass  availaltle  with 
which  to  produce  beat  in  the  sun,  and  if  this  mass  were  of  the  best 
poasible  materials  to  produce  heal  by  burning,  it  cua  be  Khown  that, 
by  burning  it  at  the  surface  of  the  sun,  we  should  pntduce  vastly 
less  heat  than  if  we  simply  allowed  it  to  fall  into  the  sun.  In  the 
iMt  caae,  if  it  fell  from  the  earth's  distance,  It  would  give  0000  times 
man  beat  by  its  fall  than  by  its  burning. 

:  ne  teait  velocity  with  which  a  body  from  space  could  fall  upon 
^  sub's  surfMe  it  In  the  neighborhood  of  .SM  nilee  in  a  leoond  of 


JSSSWB 


igi«a^^ai*«Sijii(«!^fe,-ia» 


<>SiyMM&;; 


218 


ASTRONOMY. 


'I 


•• 


I;! 


uSSi 


time,  snd  the  Telocity  may  be  as  great  as  850  miles.  The  meteoric 
theory  of  solar  heat  is  in  effect  that  the  heat  of  the  sun  is  kept  up  by 
the  impact  of  meteors  upon  its  surface. 

No  doubt  immense  numbers  of  meteorites  fall  into  the  sun  daily 
and  hourly,  and  to  each  one  of  them  a  certain  considerable  portion 
of  heat  is  due.  It  is  found  that,  to  account  for  the  present  amount  of 
radiation,  meteorites  equal  In  mass  to  the  whole  earth  would  have  to 
fall  into  the  sun  every  century.  It  is  extremely  improbable  that  a 
mass  one  tenth  as  large  as  this  is  added  to  the  sun  in  this  way  per 
century,  if  for  no  other  reason  because  the  earth  itself  and  every 
planet  would  receive  far  more  than  its  present  share  of  meteorites, 
and  would  become  quite  hot  from  this  cause  alone. 

There  is  still  another  way  of  accounting  for  the  tun's  constant 
supply  of  energy,  and  this  has  the  advantage  of  appealing  to  no  cause 
outside  of  the  sun  itself  in  the  explanation.  It  is  by  supposing  the 
heat,  light,  etc.,  to  be  generated  by  a  constant  and  gradual  contrac- 
tion of  the  dimensions  of  the  solar  sphere.  As  the  globe  cools  by 
radiation  into  space,  it  must  contract.  In  so  contracting  its  ultimate 
constituent  parts  are  drawn  nearer  together  by  their  mutuhl  attrac- 
tion, whereby  a  form  of  energy  is  developed  which  can  be  trans- 
formed into  heat,  light,  electricity,  or  other  physical  forces. 

This  theory  is  in  complete  agreement  with  the  known  laws  of 
force.  It  also  admits  of  precise  comparison  with  facts,  since  the 
laws  of  heat  enable  us,  from  the  known  amount  of  heat  radiated,  to 
infer  the  exact  amount  of  contraction  in  inches  which  the  linear 
dimensions  of  the  sun  must  undergo  in  order  tliat  this  supply  of  heat 
may  be  kept  unchanged,  as  it  is  practically  found  to  be.  With  the 
present  size  of  the  sun,  it  is  found  that  it  is  only  necessary  to  sup- 
pose that  its  diameter  is  diminishing  at  the  rate  of  about  220  feet  per 
year,  or  4  miles  per  century,  in  order  that  the  supply  of  heat  radiated 
shall  be  constant.  It  is  plain  that  such  a  change  as  this  may  be 
taking  place,  since  we  possess  no  instruments  suffleiently  delicate  to 
have  detected  a  change  of  even  ten  times  this  amount  since  the  in- 
vention of  the  telescope. 

It  may  seem  a  paradoxical  conclusion  that  the  cooling  of  a  body 
may  cause  it  to  become  hotter.  This  indeed  is  true  only  when  we 
suppose  the  interior  to  be  gaseous,  and  not  solid  or  liquid.  It  it, 
however,  proved  by  theory  that  this  law  holds  for  gaseous  i 


We  cannot  say  whisther  the  sun  has  yet  begun  to  liqtief| 
in  his  interior  parts^and  hence  it  is  impossible  to  predict, 
at  present  the  duration  of  his  constant  radii^on.    Theorjr 


3W!; 


I 


TUB  SUN, 


819 


les.  The  meteorie 
» sun  ia  kept  up  by 

into  the  sun  daily 
insiderable  portion 
present  amount  of 
u-th  would  have  to 
improbable  that  a 
un  in  this  way  per 
h  itself  and  every 
bare  of  meteorites, 

the  sun's  constant 
pealing  to  no  cause 
B  by  supposing  the 
id  gradual  contrac- 
the  globe  cools  by 
racting  its  ultimate 
lieir  mutual  attrac- 
lich  can  be  trans* 
»1  forces, 
le  known  laws  of 
Ih  facts,  since  the 
if  beat  radiated,  to 
I  which  the  linear 
this  supply  of  heat 
d  to  be.  With  the 
Y  necessary  to  sup- 
about  220  feet  per 
)ly  of  heat  radiated 
ge  as  this  may  be 
Iciently  delicate  to 
[ount  since  the  in- 
cooling  of  a  body 
true  only  when  we 
I  or  liquid.  It  it, 
gaseous  masses.  ' 

twgnn  to  liqtie^; 
«8ible  to  predict 
ii^on.    Thaorjf 


shows  us  that  after  about  5,000,000  years,  the  stin  radiat- 
ing heat  as  at  present,  and  still  remaining  gaseous,  will  be 
reduced  to  one  half  of  his  present  yolnme.  It  seems  prob* 
able  that  somewhere  about  this  time  the  solidification  will 
hare  began,  and  it  is  roughly  estimated,  from  this  line  of 
argument,  that  the  present  conditions  of  heat  radiation 
cannot  last  greatly  over  10,000,000  years. 

The  future  of  the  sun  (and  hence  of  the  earth)  cannot, 
as  y)Q  see,  be  traced  with  great  exactitude.  The  past  can 
be  more  closely  followed  if  we  assume  (which  is  tolerably 
safe)  that  the  sun  up  to  the  present  has  been  a  gaseous  and 
not  a  solid  or  liquid  mass.  Four  hundred  years  ago,  then, 
the  snn  was  about  16  miles  greater  in  diameter  than  now; 
and  if  we  suppose  this  process  of  contraction  to  have  regu- 
larly gone  on  at  the  same  rate  (an  uncertain  supposition), 
we  can  fix  a  date  when  the  sun  filled  any  given  space,  out 
even  to  the  orbit  of  Neptune;  that  is,  to  the  time  when 
the  solar  system  consisted  of  but  one  body,  and  that  a  gas- 
eous or  nebulous  one.  It  will  subsequently  be  seen  that 
the  ideas  here  reached  d  posteriori  have  a  striking  analogy 
to  the  h  priori  ideas  of  Kant  and  La  Place. 

It  is  not  to  be  taken  for  granted,  however,  that  the 
amount  of  heat  to  be  derived  from  the  contraction  of  the 
sun's  dimensions  is  infinite,  no  matter  how  large  the  prim- 
itive dimensions  may  have  been.  A  body  fallin^^  from  any 
distance  to  the  snn  can  only  have  a  certain  finiie  velocity 
depending  on  this  distance  and  the  mass  of  the  sun  itself, 
which,  even  if  the  fall  be  from  an  infinite  distance,  cannot 
exceed,  for  the  sun,  350  miles  per  second.  In  the  same 
way  the  amount  of  heat  generated  by  the  contraction  of  the 
sun's  Tolnme  from  any  size  to  any  other  is  finite  and  not 
infinite. 


MO 


ABTRONOMY. 


!:• 


It  has  been  shown  that  if  the  sun  has  always  been  radi> 
ating  heat  at  its  present  rate,  and  if  it  had  originally  filled 
all  space,  it  has  required  18,000,000  years  tu  contract  to  its 
present  volume.  In  other  words,  assuming  the  present 
rate  of  nuliution,  and  taking  the  most  faTorable  case,  the 
age  of  the  sun  docs  not  exceed  18,000,000  years.  The 
earth  is,  of  course,  less  aged.  The  supposition  lying  at 
the  base  of  this  estimate  is  that  the  radiation  of  the  sun 
has  been  constant  thronghont  the  whole  period.  This  u 
quite  unlikely,  and  any  changes  in  this  datum  affect  greatly 
the  final  number  of  years  wiiich  wo  have  assigned.  While 
this  number  may  be  greatly  in  error,  yet  the  method  of 
obtaining  it  seems,  in  the  present  state  of  science,  to  be 
satisfactory,  and  the  main  conclusion  remains  that  the  {Nist 
of  the  sun  is  finite,  and  that  in  all  probability  its  fntnro  is 
a  limited  one.  The  exact  number  of  centuries  that  it  is  to 
last  are  of  no  moment  even  were  the  data  at  hand  to  obtain 
them:  the  essential  ]i.-)int  is  that,  so  far  as  we  can  see,  the 
sun,  and  incidentally  the  solar  system,  has  a  finite  past  and 
a  limited  fntnro,  and  that,  like  other  natural  objects,  it 
passes  through  its  regular  stages  of  birth,  vigor,  decay,  and 
death,  in  one  order  of  progress. 


mmmm 


•«mJ-;  ..  itn 


I 


ilways  been  radU 
I  originally  filled 
to  contract  to  its 
ling  the  present 
▼orablo  case,  the 
KK)  years.  Tlio 
osition  lying  at 
Ation  of  the  sun 
period.  This  m 
um  affect  greatly 
ssigncd.  While 
i  the  method  of 
>f  science,  to  be 
jns  that  the  ]>a8t 
ility  its  fntnro  is 
irics  that  it  is  to 
it  hand  to  obtain 
I  we  can  see,  the 
a  finite  past  and 
tnral  objects,  it 
rigor,  decay,  and 


OHAPTER  in. 
THE  INFERIOR  PLANETB. 

Monovi  An  AfPionL 

Trb  Infflrio  planets  are  those  whose  orbits  lie  between  the  sun 
and  the  orbit  of  the  earth.  Commencing  with  the  more  distant  ones, 
they  comprise  Vtnu*  and  Mercury. 

The  real  and  apparent  moiiuns  of  these  planets  have  already  been 
briefly  described  in  Part  I.,  Chapter  V.  It  will  be  rememliered  that, 
in  accordance  with  Keflkb's  third  law,  their  periods  of  revolution 
around  the  sun  are  less  tlun  that  of  the  earth.  Consequently  they 
OTertalte  the  latter  lietween  suocewive  inferior  conjunctions. 

The  interval  between  these 
conjunctions  is  about  four 
months  in  the  case  of  Mer- 
cury, and  between  nineteen 
and  twenty  mouths  in  (hat  of 
Yentu.  At  the  end  of  this 
period  each  repeats  the  same 
series  of  motions  relative  to 
the  sun.  What  these  motion* 
are  can  be  rendily  seen  by 
studying  Fig.  95.  In  the  first 
place,  suppose  llie  earth  at 
any  pioint,  S,  of  iu  orliit,  and 
if  we  draw  a  line.  E  L  at 
EM,  from  E.  tangent  to  the 
orUt  of  either  of  tliese  planets, 
it  is  evident  that  the  angle 
which  this  line  malies  with  that  drawn  to  the  sun  is  the  greatest 
elongation  of  the  planet  from  the  sun.  The  orbits  being  eccentric, 
thk  elongaUim  varies  with  the  position  of  the  earth.  In  the  case 
of  JTsrswy  it  rsages  from  16*  to  86*,  while  ia  the  esse  of  Vetuu,  V- 
oiMt  of  whicfa  is  nearly  circular,  it  varies  very  little  from  45*.  TbjS'O 
phaets,  tiwrefote,  seem  to  have  an  cscUladog  motion,  first  swiofiBf 


Ito.  a& 


^appi^iFiiw 


9M 


A8TROK0M7. 


Wta.  M.— Appamsiit  MAamrrou 
am  TMM  DuK  or  MiaoiniT. 


toward  the  east  of  the  sun,  and  then  toward  the  west  of  it,  as  already 
explained.  Since,  owing  to  the  annual  revolution  of  the  earth,  the 
sun  has  a  constant  eastward  motion  among  the  stars,  these  planets 
must  haTe,  on  tlie  whole,  a  corresponding  though  intermittent  motion 
in  the  same  direction.  Therefore  the  ancient  astronomers  supposed 
their  period  of  revolution  to  be  one  year,  the  same  as  that  of  the 
sun. 

If,  agahi,  we  draw  a  line  ESC  from  tlie  earth  through  the  sun,  the 
point  /,  in  which  this  line  cute  tiie  orbit  of  the  planet,  or  the  point 
of  inferior  conjunction,  will  be  the  least  distance  of  the  planet  from 

the  earth,  while  the  second  point  C, 
or  the  point  of  superior  conjuiiclion, 
on  the  opposite  side  of  the  sun,  will 
be  the  greatest  distance.  Owing  to 
tlie  difference  of  these  distances  the 
apparent  magnitude  of  these  planets, 
as  seen  from  iho  earth,  is  subject  to 
great  variations. 
Fig.  66  shows  thcMS  variations  in  the 
ease  of  Mnvurjf,  A  representing  its  apparent  magnitude  when  at  its 
greatest  distance,  B  when  nt  its  mean  distance,  and  C  when  at  ito 
least  distance.  In  the  cose  of  Venut  (Fig.  67)  the  variations  are  much 
greater  than  in  that  of  Mercury,  the  greatest  distence.  1.73,  being 
more  than  six  times  the  least  distance,  which  is  only  0.28.  Tiie 
variations  jf  apparent  magnitude  are  therefore  great  in  the  same 
proportion. 

In  thus  representing  the  apparent  angular  magnitude  of  these 
planets,  we  suppose  their  whole  dislcs  to  be  visible,  as  they  would  be 
if  they  shone  by  their  own  light  But  since  they  can  be  seen  only  by 
the  reflected  light  of  the  sun,  only  those  portions  of  the  disk  can  be 
seen  which  are  at  the  same  time  visible  from  the  sun  and  from  the 
earth.  A  very  little  consideration  will  show  that  the  proportion  of 
the  dbk  which  can  be  seen  constently  diminishes  as  the  planet  ap- 
proaches the  earth,  and  looks  larger. 

When  the  planet  is  at  ita  greatest  distance,  or  in  superior  conjunction 
(0,  Fig.  65),  lu  whole  illuminated  hemisphere  can  be  seen  from  the 
earth.  As  it  moves  around  and  approaches  the  earth,  the  illuminated 
hemisphere  is  gradually  turned  from  us.  At  the  point  of  greatest 
elongation,  M  or  L,  one  half  the  hemisphere  is  visible,  and  the 
planet  has  the  form  of  the  moon  at  first  or:second  quarter^  At  it 
«l>proachea  inferior  conjunction,  the  apparent  visible  disk  aasumea 
the  form  of  a  crescent,  which  becomes  thinner  and  thinner  as  tba 
|danet  approMhea4lie  aun. 


westof  it,  M  already 
Ion  of  the  earth,  the 
I  stars,  these  planets 
I  intermittent  notion 
itronomers  supposed 
same  as  that  of  the 

through  the  sun,  the 

planet,  or  the  point 

e  of  the  planet  from 

the  second  point  C, 

iperior  conjunction, 

lide  of  the  sun,  will 

distance.    Owing  to 

these  distances  the 

ido  of  these  planets, 

earth,  is  subject  to 

be«)  variations  in  the 
lagnitude  when  at  its 
I,  and  G  when  at  its 
I  variations  are  much 
distance,  1.73,  being 
\\  is  only  0.28.  Tlie 
e  great  in  the  same 

magnitude  of  these 
l>lc,  as  they  would  be 
y  can  be  seen  only  by 
ns  of  the  disk  can  Im 
le  sun  and  from  the 
lat  the  proportion  of 
lies  as  Uie  planet  ap- 

i  superior  conjunction 
Ban  be  seen  from  the 
earth,  the  illuminated 
he  point  of  greateat 
)  is  visible,  and  the 
cond  quarter  As  it 
visible  disk  assumes 
r  and  thinner  at  the 


THK  INFERIOR  PLANETS. 


Fig  68  shows  the  apparent  disk  of  Jforeufjr  at  various  times  during 
iU  synodic  revolution.  The  planet  will  appear  brightest  when  this 
dUk  lins  the  greatest  surface.  This  occurs  about  half  way  between 
greatest  elongation  and  inferior  conjunction. 

In  consequence  of  the  changes  in  the  brilliancy  of  these  plancU 
produced  by  the  variations  of  distance,  and  those  produced  by  the 


Fio.  ar.-AMPiMWT  MMimvDn  of  ma  Dme  o»  Vamm. 


variations  in  the  proportion  of  illuirinated  disk  virible  from  the 
earth,  partially  compensating  each  oUier,  their  actual  brilliancyto 
not  subject  to  such  great  variations  as  might  have  been  expectMl. 
As  a  genend  rule,  Mercury  shines  with  a  light  exceeding  that  of  a 
■Ur  of  the  first  magnitude.    But  owing  to  iU  proximity  to  the  sun, 


•       I      ) 

•  «  (  ( 


Ito.  M.— Amuuiraa  or  Maaoaav  at  Dvnanr  FonRa  or  ns  Oaarr. 

It  can  never  be  seen  by  the  naked  eye  except  in  the  west  a  short  time 
after  sunset,  and  In  tiie  east  a  little  before  sunrise.  It  is  then  of 
necessity  near  the  horixon.  and  therefore  does  not  seem  so  bright  aa 
If  It  were  at  a  greater  altitude.  In  our  latitudes  we  mi^t  almoat 
lav  that  It  is  never  ▼UUo  except  la  the  monilDf  or  evenlog  twilight 


994 


ASTRONOMT. 


i\ 


On  the  other  hand,  the  plnnet  Venua  is,  next  to  the  inn  and  moon, 
the  moat  brilliant  object  in  tlie  heavens.  It  is  so  much  brijrhter 
than  any  fixed  star  that  there  can  seldom  be  any  difllculiy  in  identi- 
fying it.  The  unprac(i:*ed  observer  might  under  some  oircumatances 
find  a  difficulty  in  distinguishing  between  Venut  and  JupiUr.  but 
the  different  motions  of  tiie  two  pluneU  will  enable  him  to  distin- 
guish tliem  if  they  are  watched  from  night  to  night  during  several 
weeiis. 

Atmoiphiu  um  Rotatiov  or  Mibovit. 

The  various  phases  of  Mercury,  as  dependent  upon  iu  rarious 
positions  rohttive  to  the  sun,  liuve  already  been  shown.  If  the  planet 
were  an  opnque  sphere,  witliout  inequalities  and  witiiout  an  atmos- 
phere, the  apparent  disk  would  always  be  bounded  by  a  circle  on 
one  side  and  an  ellipse  on  the  other,  as  represented  in  the  flgtire. 
Whether  any  variation  from  this  simple  and  perfect  form  has  ever 
been  detected  is  an  open  question,  the  balance  of  evidence  being  very 
strongly  in  the- negative.  Since  no  spots  are  visible  upon  It.  it  would 
follow  that  unless  variations  of  form  due  to  inequalities  on  its  sur- 
face, such  as  mountains,  can  bo  dcti-cted,  it  ia  Impossible  to  deter- 
mine whether  tlie  planet  rotates  on  its  axis. 

We  may  reganl  it  as  doubtful  whether  any  evidence  of  nn  atmos- 
phcrc  of  Mercury  lias  been  obtained,  and  it  is  certain  that  we  know 
nothing  definite  respecting  its  physical  constitution. 

ATMosPHni  An  BoTAnov  ov  Ymu. 

As  Venu$  somvlinies  comes  nearer  the  earth  than  any  other  pri- 
mary planet,  astronomers  have  examined  its  snrface  witli  great  at- 
tention ever  since  tlie  invention  of  thct  telescope.  But  no  concliisive 
evidence  respecting  tlie  rotation  of  (he  piniat  and  no  proof  of  any 
changes  or  any  inequalities  on  its  furface  have  ever  been  obtained. 

Atmoiphare  ef  Taans.— The  evidence  of  nn  atmoepliere  of  V»mv$  is 
licrliaps  more  eonclusivo  than  in  tlic  case  of  any  ntlier  planet. 
When  Vetiua  is  observed  very  near  its  inferior  oonjnnction,  and 
when  it  therefore  prescnto  the  view  of  a  very  thin  crcsrent,  it  is 
found  that  this  crescent  extends  oyer  moro  than  |80*.  This  wouhi 
lie  evidently  inipoMibie  unless  the  sun  illuminated  more  than  ooff 
half  the  planet.  We  therefore  conclude  that  Venm$  hlia  an  Mmoa- 
phere  whicii  exercises  so  powerful  a  refraction  upon  the  liglit  of  the 
sun  that  the  latter  illuminates  several  degrees  more  than  one  half  the 
globe.  A  phenomenon  whicii  muf>t  be  attributed  to  the  same  cause 
b»»  s«)f epal  timea  b^n  observed  during  trMi«im  9f  f^TlifA    Pnrip| 


■^'«llili»IIIMWtllii|«MHW1llt<IB«MM^^ 


EWft»»' 


\o  the  ■nn  and  moon, 
is  so  much  brijrhter 
y  difRcuUy  in  identl- 
r  sume  oircumsUuces 
itt<  and  JupiUr.  but 
nable  him  to  distin- 
light  during  several 

KnouiT. 

at  upon  iu  rarious 
liown.  ir  the  planet 
d  witliout  an  ntmos- 
nded  hy  a  circle  on 
lentcd  in  the  flgnre. 
rfect  form  has  ever 
evidence  being  very 
ble  upon  it,  it  would 
equnlities  on  its  sur- 
impossible  to  deter- 

vidcnce  of  nn  atmoa- 
ertain  that  we  Itnow 
ion. 

r  ysvni 

thnn  any  other  pri- 
rfnco  Willi  great  at- 
But  no  conchisive 
tind  no  proof  of  any 
vrr  been  obtained, 
noephoreof  FSraMis 
!  any  oilier  planet, 
tr  ronjiinctinn,  .and 
thin  crcsTpnt,  it  is 
I  180*.  This  would 
ftted  more  than  oop 
'*nv$  hi*  an  Mmoa- 
ipon  the  light  of  the 
>re  than  one  half  the 
9d  to  the  same  cause 
9ff«»Hf«.    Pnrip| 


I 


TUB  iNrwrnon  PiANSTa. 


tiM  tnoiit  of  December  8th,  1874,  most  of  the  observers  who  enjoyrd 
%  line  steady  atmosphere  saw  that  when  Vtnu$  was  partially  pro- 
jected on  the  sun,  the  outllfie  of  that  part  of  its  disk  outside  the  sun 
could  be  distinguished  by  a  delicate  line  of  light.  From  these 
several  obser^ationa  It  would  seem  that  the  refractive  power  of  the 
atmosphere  of  Fmim  Is  greater  than  that  of  the  earth. 

Teabirs  or  MftBovBT  An  Vivm. 

When  JKMViHy  or  Ymut  peases  between  the  earth  and  sun,  so  as 
to  appear  projeelad  on  the  sun's  disk,  the  phenomenon  Is  called  a 
trmntU.  If  these  planets  moved  around  the  ann  in  the  plane  of  the 
ecliptic,  it  la  evident  that  there  would  be  a  transit  at  every  inferior 
conjunction. 

The  longitude  of  the  deacending  node  of  Mmnmrjf  at  the  preaent 
time  is  227°,  and  therefore  that  of  the  aareading  node  47'.  Tiie 
earth  has  these  longitudes  on  May  7lb  and  November  9lh.  Since  a 
transit  can  occur  only  within  a  few  degrees  of  a  node,  M«reur}f  cau 
transit  oitly  within  a  few  days  of  tliese  cpocha. 

The  longitude  of  tlie  descending  node  of  Vtnui  is  now  about  808^ 
and  therefore  that  of  the  aMMnding  node  is  76*.  The  earth  has  theat 
longitudes  on  June  8th  and  Decismber  7th  of  each  year.    Transits  of 
Venut  ean  therefore  oeeur  only  within  two  or  three  daya  of  these 


I  ef  Traasits  sf  Msreiry.— The  following  table  shows  the 
dates  of  occurrence  of  tranaits  of  Mtreury  during  the  present  cen- 
tury. Tliey  are  separated  into  May  transiu,  which  occur  near  tlie 
descending  node,  and  November  once,  which  occur  near  the  ascend- 
inir  node.  November  trannits  are  the  most  numeroua,  because 
JUratry  is  then  nearer  the  sun,  and  the  transit  limita  are  wider. 

1798,  May  8.  1802,  Nov.   9. 

1889,  May  8.  1818.  Nov.  11. 

}84t.  May  8.  1888,  Nov.   S. 

18T8.  May  «.  1888.  Nov.   7. 

1881,  May  9.  1848,  Nov.  10. 

1881.  Nov.  18. 

1808,  Nov.   5. 

1881,  Not.   7. 

18B4,  Nov.  10. 

s(  Traaafts  af  TesM.— For  many  oenturiea  paat  and  to 

wmx  »w»»l«»  of  r«»*M  ocdir  in  »  cycle  mor*  ^xnvi  *•»  rtoie  of 


■imii»mm; 


I 


S36 


ABTRONOMT. 


N 


?:; 


d 


Mercury.  It  happens  that  F«n««  makes  18  reTolutions  sround  the 
■un  ia  nearly  the  aame  time  that  (he  earth  makes  8  revolutions;  that 
is,  in  eight  years.  During  this  period  there  will  be  S  inferior  con< 
junctions  of  Venut,  because  the  latter  has  trade  5  revolutions  more 
than  the  earth.  Consequently,  if  we  wait  sight  years  from  an  inferior 
conjunction  of  Venu$,  we  shall,  at  the  end  of  tliat  time,  have  another 
Inferior  conjunction,  the  fifth  in  regular  order,  at  nearly  the  same 
point  of  the  two  orbits.  It  will,  therefore,  occur  at  the  same  time 
of  tiie  year,  and  in  nearly  the  same  position  relative  to  the  node  of 
Venut. 

After  a  pair  of  transits  8  years  apart,  an  interval  of  over  100  years 
must  elapse  before  the  occurrence  of  another  pair  as  is  shown  in  the 
following  tabic.  The  dates  and  intervals  of  the  transiU  for  three 
cycles  nearest  to  the  present  time  are  as  follows: 

Interrals. 
1518,  June  3.  1761,  June  5.  3004,  June  8  8  years. 


1526,  June  1. 
1681,  Dec.  7. 
168»,  Dec.  4. 


1760,  Junes. 
1874,  Dec.  0. 
1883,  Dec.  6. 


!»>13,  June  6.         105i 
2117,  Dec.  11.  8 

31S6,  Dec.  8  131i 


SVPrOOD  IXTBAMBBOinUAL  PlAHlTI. 

Some  astronomers  are  of  opinion  tliat  there  is  a  small  planet  or 
a  group  of  planets  revolving  around  the  sun  inside  th-..  orbit  of 
Mercury.  To  this  supposed  planet  the  name  Vvkan  has  Ix^n  given; 
but  astronomers  generally  discredit  the  existence  of  any  such  planet 
of  considerable  size. 

The  evidence  in  favor  of  the  existence  of  such  planets  may  be 
divided  into  three  classes,  as  follows,  whiub  will  be  considered  in 
their  order: 

(1)  A  motion  of  the  perihelion  of  the  orbit  of  Mercury,  supposed 
to  be  due  to  the  attraction  of  such  a  planet  or  group  of  planets. 

CD  Transits  of  dark  bodieti  acrqss  the  disk  of  the  sun  which  have 
Inen  supposed  to  be  seen  by  varans  observers  during  the  past  cen- 
tury. 

(8)  TIm  obeervation  of  certain  unidentified  objects  by  Professor 
Watson  and  Mr.  Lbwib  Swirr  during  the  total  eclipse  of  the  sun, 
July  28tb,  1878. 

(1)  In  1858  Lb  Verribb  made  a  jareful  collection  of  all  the  obser- 
vations on  the  transits  of  Mercury  which  had  been  recorded  since  the 
invention  of  the  telescope.     The  result  of  that  investigation  waa 


BJtWMIOTMWiiil 


'olutioDi  around  the 
s  8  revolutions;  that 
III  be  5  inferior  con< 
e  6  revolutioni  more 
ears  from  an  inferior 
It  time,  have  another 
at  nearly  the  same 
iur  at  the  same  time 
ttive  to  the  node  of 

val  of  over  100  years 
>lr  as  is  shown  in  the 
Ihe  transits  for  three 


neS 
me  9. 

ic.  11. 
X.B 


Intwrrals, 
8  years. 

lOIH    " 

8      " 

laii    " 


I  is  a  small  planet  or 

inside  th-.  orbit  of 

\tkan  has  Ix^en  given; 

»  of  any  such  planet 

luch  planets  may  be 
viU  be  considered  in 

Df  Mermry,  supposed 
roup  of  planets. 
f  the  sun  which  have 
I  during  the  past  cen- 

objects  by  Professor 
tal  eclipse  of  the  sun, 

etion  of  all  the  obser- 
•n  recorded  since  the 
tat  investigation  waa 


■T-» 


THE  INFERIOR  PLANETS. 


227 


that  the  observed  times  of  transit  could  not  bo  reconciled  with  the 
calculated  motion  of  tho  planet,  as  duo  to  the  gravitation  of  the 
other  bodieii  of  the  solar  system.  He  found,  however,  that  if,  in 
addition  to  the  changes  of  the  orbit  due  to  the  attraction  of  the 
known  plauets,  he  supposed  a  motion  of  the  perihelion  amounting  to 
80 '  ill  a  century,  the  observations  could  all  be  satisfied.  Such  a 
motion  might  be  produced  by  the  attraction  of  an  unlinown  planet 
inside  the  orbit  of  Mercury.  Since,  however,  a  single  planet,  in 
order  to  produce  this  effect,  would  have  to  be  of  considerable  size, 
and  since  no  such  object  had  ever  been  observed  during  a  total 
eclipse  of  the  sun,  he  concluded  that  there  was  prolwbly  a  group  of 
planets  much  too  small  to  be  separately  distinguislied. 

(3)  It  is  to  be  noted  that  if  such  planeU  existed  they  would  fre- 
quently pass  over  the  disk  of  the  sun.  During  the  past  fifty  years 
the  sun  has  been  observed  almost  every  day  with  the  greatest 
assiduity  by  eminent  observers,  armed  with  powerful  instruments, 
who  have  made  the  study  of  the  sun's  surface  and  spots  the  principal 
work  of  their  lives.  None  of  these  observers  has  ever  recorded  the 
transit  of  an  unknown  planet.  This  evidence,  though  negative  in 
form,  is,  under  the  circumstances,  conclusive  against  tlie  existence 
of  such  a  planet  of  such  magnit-ide  as  to  be  visible  in  transit  with 
ordinary  instruments. 

(8)  The  observations  of  Professor  Watbom  during  the  total  eclipse 
above  mentioned  seem  to  afford  the  strongest  evidence  yet  obtained 
in  favor  of  the  real  existence  of  the  planet  His  mode  of  proceeding 
was  briefly  this:  Sweeping  to  the  west  of  the  sun  during  the  eclipse, 
he  saw  two  objects  in  positions  where,  supposing  the  pointing  of  bis 
telescope  accurately  known,  no  fixed  star  existed.  There  is,  how. 
ever,  a  pair  of  known  stars,  one  of  which  is  about  a  degree  distant 
from  one  of  the  unknown  objects,  nnd  tlie  other  about  the  same 
distance  and  direction  from  the  second.  It  is  probable  that  Professor 
Watsoh 'a  supposed  pUnots  were  this  pair  of  stan. 

Since  the  above  was  written  Prof.  Watboh'b  observations  have 
been  repeated  under  exceptionally  favorable  circumstances  at  the 
eclipse  of  May  6. 1888,  and  no  trace  of  his  supposed  planets  was  seen, 
while  much  smaller  stars  were  observed. 


ii 


i 


I'l 


I 


i  :i' 


/ 


aiiiiL 


CHAPrER  IV. 


THE  MOON. 


Whrn  it  became  clearly  understood  that  the  earth  and 
moon  were  to  be  regarded  as  bodies  of  one  class,  and  thut 
the  old  notion  of  an  impassable  gulf  between  the  character 
of  bodies  celestial  and  bodies  terrestrial  was  unfounded, 
the  question  whether  tlio  moon  was  like  the  earth  in  all  its 
details  became  one  of  great  interest.  The  point  of  most 
especial  interest  was  whether  the  moon  could,  like  the 
earth,  *je  peopled  by  intelligent  inhabitants.  Accordingly, 
when  the  tcicscope  was  iuvcnted  by  Galileo,  one  of  the 
first  objects  examined  was  the  moon.  With  every  im- 
provement of  the  instrument  the  examination  became 
more  thorough,  so  that  at  present  the  topography  of  the 
moon  is  much  better  known  than  that  of  the  State  of 
Arkansas,  for  example. 

With  every  improvement  in  the  means  of  research,  it 
has  become  more  and  more  evident  that  the  surface  of  the 
moon  is  totally  unlike  that  of  our  earth.  There  are  no 
oceans,  seaa,  rivers,  air,  clouds,  or  vapor.  We  can  hardly 
suppose  that  anime*  '^r  vegetable  life  exists  under  such  cir- 
cumstances, the  funu«.mental  ooqditions  of  raoh  existence 
on  our  earth  being  entirely  wanting,  We  might  almoit  ai 
well  suppose  a  piece  of  granite  or  lay»  to  be  the  abode  of 
life  OS  the  surface  of  the  moon. 

The  l«n|^h  of  one  mile  on  the  moon  would,  m  wen  from 


iiNiwwiiaiwrtfMtiiW^^ 


-rn 


at  the  earth  and 
le  clan,  and  that 
een  the  character 

was  unfounded, 
he  earth  in  all  ita 
he  point  of  most 
1  could,  like  the 
ts.  Accordingly, 
JLEo,  one  of  the 

With  every  im- 
mination  became 
opography  of  the 
b  of  the  State  of 

ns  of  research,  it 
the  surface  of  the 
b.  There  are  no 
We  can  hardly 
ts  under  such  oir< 
of  inoh  existence 
9  might  almost  as 
o  be  the  abode  of 

)nld,  M  wen  froni 


TSB  MOON. 


339 


the  earth,  subtend  an  angle  of  about  1*  of  arc.  More 
exactly,  the  angle  subtended  would  range  between  0'.8  and 
O'.O,  juscording  to  the  varying  distance  of  the  moon.  In 
order  that  an  object  may  be  plainly  vIsIIjIo  to  the  naked 
eye,  it  must  subtond  an  angle  of  nearly  1'.  Consequently 
a  magnifying  power  of  60  is  required  to  render  a  round 
object  one  mile  in  diameter  on  the  surface  of  the  moon 
plainly  visible.  Starting  from  this  fact,  we  may  readily 
form  the  following  u.jie,  showing  the  diameters  of  the 
smallest  objects  that  can  be  seen  with  different  magnifying 
powers,  always  assuming  that  vision* with  these  powers  is 
perfect: 

Power     60;  diameter  of  object  1  mile. 

Power   IfiO;  diuneter  2000  feet 

Power  800;  diameter  600  feet  ■ 

Power  tOOO;  diemeter  8U0  feet. 

Power  9000;  diameter  100  feet 

If  telescopic  power  could  he  increased  indefinitely,  there 
would  of  course  be  no  limit  to  the  minuteness  of  an  object 
visible  on  the  moon's  surface.  But  the  necessary  imper- 
fections of  all  telescopes  are  such  that  only  in  extraordinary 
oases  can  anything  be  gained  by  increasing  the  magnifying 
power  beyond  1000.  The  influence  of  warm  and  cold  cur- 
rents in  our  atmosphere  will  forever  prevent  the  advan- 
tageous use  of  high  magnifying  powers.  After  a  certain 
limit  we  see  nothing  more  by  increasing  the  power,  vision 
becoming  indistinct  in  proportion  as  the  fower  is  increased. 
It  is  hardly  likely  that  an  object  less  than  600  feet  in  extent 
can  ever  be  seen  on  the  moon  by  any  telescope  whatever, 
unless  it  becomes  possible  to  mount  the  instrument  above 
the  atmosphere  of  the  earth.  It  is  therafore  only  the  great 
Itatures  on  the  rarfaoe  of  the  moon,  and  not  the  miiint« 
ones,  which  can  be  nwde  out  with  the  telescope. 


■  .■■it^ii^l^ttKSff^sU0$S^\ 


i 


I  'I 


980 


ABTRONOMT. 


:5s 


fta.  691— Aanor  or  nn  Mboii's  SnurMB. 

OhMMUr  «f  tht  Mem'i  luliMa.— The  moat  atriking  point  of  dif- 
ference between  tlio  earth  and  moon  ia  aeen  in  the  total  abaence  frrai 
the  latter  of  anything  that  loolu  like  an  undulating  aurfaea.    No 


■.■^^'iT?ilB«MMWii«WrtffllMii<i 


tanKBgifaKa^ 


-.)  '^^.      { 


THE  MOON. 


S81 


nVMB. 


Striking  point  of  dif- 
tlie  total  abaenoe  from 
lulating  saiikca.    Ko 


S^^ 


formations  similar  to  our  valleys  and  mountain-cIiaiuB  have  l)een 
detected.  Tbe  lowest  surface  of  the  moon  whicli  can  lie  seen  witli 
the  telesco]M3  uppears  to  \m  nearly  smootli  and  flat,  or,  to  spealc 
more  exactly,  splierical  (l)ecause  tlie  moon  is  a  sphere).  This  sur- 
face has  different  shades  of  color  in  different  regions.  Some  por- 
tions are  of  a  bright  silvery  tint,  while  others  have  a  dark  gray  ap- 
pearance. These  differences  of  tint  seem  to  arise  from  differences  of 
material. 

Upon  this  surface  as  a  foundation  are  built  numerous  formations 
of  various  sizes,  but  all  of  a  very  simple  character.  Their  general 
form  can  be  made  out  by  the  aid  of  Fig.  68,  and  their  dimensions  by 
tlie  scale  of  miles  at  the  bottom  of  it.  Tiie  largest  and  most  promi- 
nent features  are  known  as  craters.  They  liave  a  typical  form  con- 
sisting  of  a  round  or  oval  rugged  wall  rising  from  the  plane  in  the 
manner  of  a  circular  fortification.  These  walls  arc  frequently  from 
three  to  six  thousand  metres  in  height,  very  rough  and  broken.  In 
their  interior  we  see  the  plane  surface  of  the  moon  already  described. 
It  is,  Iiowever,  generally  covered  with  fragments  or  broken  up  by 
small  inequalities  so  as  not  to  be  easily  made  out.  In  the  centre  of 
the  craters  we  frequently  find  a  conical  formation  rising  up  to  a  con- 
siderable Iielght,  and  much  larger  than  tbe  inequalities  just  described. 
In  the  craters  we  have  a  vague  resemblance  to  volcanic  formations 
upon  the  eartli,  the  principal  difference  Iieing  that  their  magnitude  is 
very  much  greater  than  anything  known  here.  The  diameter  of  the 
larger  ones  ranges  from  60  to  200  kilometres,  while  the  smallest  are 
so  minute  as  to  be  hardly  visible  with  tbe  telescope. 

When  the  moon  is  only  a  few  days  old,  the  sun's  nys  strike  very 
obliquely  upon  tiie  lunar  mountains,  and  they  cast  long  shadows. 
From  the  known  petition  of  tlie  sun,  moon,  and  earth,  and  from  the 
measured  length  of  these  shadows,  the  heights  of  the  mountains  can 
be  calculated.  It  is  thus  found  that  some  of  the  mountains  near  tbe 
south  pole  rise  to  a  height  of  8000  or  9000  metres  (from  SS.OOO  or  80,000 
feet)  above  the  general  surface  of  the  moon.  Heights  of  from  8000 
to  TiDOO  metres  are  very  common  over  almost  the  whole  lunar  surface. 

The  question  of  the  origin  of  the  lunar  features  has  a  bearing  on 
theories  of  tenestrial  geology  as  well  as  upon  various  questions  re- 
specting the  past  history  of  tlie  moon  itself.  It  has  been  considered 
in.tbis  aspect  by  various  geologists. 

Liuar  Atmosj^ars, — The  question  whether  the  moon  has  an  atmos- 
phera  has  l)een  much  discussed.  The  only  conclusion  which  has  yet 
been  reached  is  that  no  positive  evidence  of  an  atmosphere  has  ever 
been  obtained,  and  that  if  one  exists  it  is  certainly  several  hundred 
times  rarer  than  the  atmosphere  of  our  earth. 


111,1, 


I 


n 


'■    ' 


>  ■ 


11 

I 


33d 


ABTRONOMT. 


light  Mid  HMt  of  tha  Koon.— Many  attempts  have  been  made  to 
mensiirc  the  ratio  of  the  light  of  tlie  full  moon  and  that  of  the  sun. 
Tlie  rusults  have  been  very  discordant,  but  all  have  agreed  in  show- 
ing that  the  sun  emits  several  hundred  thousand  times  as  mu6h  light 
as  the  full  moon.  The  last  and  most  careful  determination  is  that  of 
ZOluibr,  who  finds  the  sun  to  be  618,000  times  as  bright  as  the  full 
moon. 

Tiio  moon  must  reflect  the  heat  as  .veil  as  the  light  of  the  sun,  and 
must  also  radiate  a  small  amount  of  its  own  heat.  By  collecting  the 
moon's  rays  in  the  focus  of  one  of  his  large  reflecting  telescopes,  Lord 
RosBB  was  able  to  show  that  a  certain  amount  of  heat  is  actually 
received  from  the  moon,  and  that  this  amount  varies  with  the  moon's 
phase,  as  it  should  do.  As  a  general  result  of  all  his  researches,  it 
may  l>e  supposed  that  about  six  sevenths  of  the  heat  given  out  by  the 
moon  is  radiated  and  one  seventh  reflected. 

Is  there  any  Ghaage  en  the  lufiMe  ef  the  Moon  1 — When  the  sur- 
face of  the  moon  was  first  found  to  be  covered  by  craters  having  the 
appearance  of  vdlcanoes  at  the  surface  of  the  earth,  it  was  very 
naturally  thought  that  these  supposed  volcanoes  might  be  still  in 
activity,  and  exhibit  themselves  to  our  telescopes  by  their  flames. 
Not  the  slightest  sound  evidence  of  any  incandescent  eruption  at  the 
moon's  surface  has  been  found,  however. 

Several  instances  of  supposed  changes  of  shape  '^'  'catvres  on  the 
moon's  surface  have  been  described  in  recent  time  . 

The  question  whether  these  changes  are  proveu  '  n  which 

the  opinions  of  aalronomers  differ.  Tlie  difficulty  c  ;  ',i  ag  a  cer- 
tain conclusion  arises  from  the  fact  that  each  feb<.u<d  necessarily 
varies  in  appearance,  owing  to  the  different  directions  in  which  the 
sun's  light  falls  upon  it.  Sometimes  the  changes  are  very  difllcult 
to  account  for,  even  when  it  is  cert^n  that  they  do  not  arise  from 
any  change  on  the  moon  itself.  Hence  while  some  regard  the  appa- 
rent changes  as  real,  others  regard  them  as  du«  only  to  differences  in 
the  mode  of  illumination. 


"flWBliBM 


aattaiWBi 


I* 


>  have  been  made  to 
md  tliat  of  the  sun. 
laye  agreed  in  show- 
I  times  as  mu6h  light 
termination  is  that  of 
as  bright  as  the  full 

light  of  the  sun,  and 
t.  By  collecting  the 
!ting  telescopes,  Lord 
at  of  heat  is  actually 
tries  with  the  moon's 
all  his  researches,  it 
iieat  eiven  out  by  the 

ion  1 — When  the  sur- 
}y  craters  having  the 
3  earth,  it  was  very 
«8  might  be  still  in 
ipcs  by  their  flames, 
scent  eruption  at  the 

pe  '!'  'catwres  on  the 
ne  . 

Dveu  '  n  which 

ty  t  '  -  '., og a  cer- 
li  feb<.u<e  necessarily 
ectlons  in  which  the 
i;es  are  very  dMBcult 
ley  do  not  arise  from 
>me  regard  the  appa- 
only  to  differences  in 


'im^ 


CHAPTER  V. 
THE  PLANET  MARS. 

Beiobiftiov  OV  THB  Flahxt. 

Mara  is  the  next  planet  beyond  the  earth  in  the  order  of 
distance  from  the  sun,  being  about  half  as  far  again  as  the 
earth.  It  has  a  decided  red  color,  by  which  it  may  bo 
readily  distinguished  from  all  the  other  planets.  Owing  to 
the  considerable  eccentricity  of  its  orbit,  its  distance,  both 
from  the  snn  and  from  the  earth,  varies  in  a  larger  propor- 
tion than  does  that  of  the  other  outer  planets. 

At  the  most  favorable  oppositions,  its  distance  from  the 
earth  is  about  0.38  of  the  astronomical  unit,  or,  in  round 
numbers,  67,000,000  kilometres  (35,000,000  of  miles). 
This  is  greater  than  the  least  distance  of  Venut,  but  we 
can  nevertheless  obtain  a  better  view  of  Mars  under  these 
circumstances  than  of  Venus,  becsuse  when  the  latter  is 
nearest  to  us  its  dark  hemisphere  is  turned  toward  n>-, 
while  in  the  case  of  Mars  and  of  the  outer  planets  tl  o 
hemisphere  turned  toward  us  at  opjwsition  is  fully  illumi- 
nated by  the  sun. 

The  period  of  revolution  of  Mars  around  the  sun  is  a 
little  less  than  two  years,  or,  more  exactly,  687  days.  The 
snoceasive  oppositions  occur  at  intervals  of  two  years  and 
one  or  two  months,  the  earth  having  made  during  this  in- 
terval a  little  more  than  two  revolutions  around  the  sun, 
wd  the  planet  Mars  a  little  more  than  one.    The  dates  of 


■'  smimmmHmmimmmmgmmi*m'- 


J  f 
■t  i 


984 


ABTRONOMT. 


seTeral  past  '^nd  f ature  oppositions  are  shown  in  tho  fol- 
lowing table: 

1881 Decemlicr  26tb. 

1884 January  81«t. 

1886 March  6lh. 

Owing  to  the  unequal  motion  of  the  planet,  arising  from 
the  eccentricity  of  its  orbit,  the  intenrals  between  suoces- 
siye  oppositions  vary  from  two  years  and  one  month  to  two 
years  and  two  and  a  half  months. 

Mara  necessarily  exhibits  phases,  but  they  are  not  lo  well 
marked  as  in  the  case  of  Venus,  because  the  hemisphere 
which  it  presents  to  the  observer  on  the  earth  is  always 
more  than  half  illuminated.  The  greatest  phase  occurs 
when  its  direction  is  90°  from  that  of  the  sun,  and  even 
then  six  serenths  of  its  disk  is  illuminated,  like  that  of  the 
moon,  three  days  before  or  after  full  moon.  The  phases 
of  Mar»  were  observed  by  Galileo  in  1610. 

B«tatioa  «r  Han.— The  early  telescopic  obeervers  noticed  that  the 
disli  of  Man  did  not  appear  uniform  in  color  and  brightnesa,  Imt 
lud  a  variegated  aspect.  In  1886  Dr.  Robbht  Hooks  found  that 
the  marliings  on  Mart  were  permanent  and  moved  around  in  such  a 
way  as  to  show  that  the  planet  revolved  on  its  axis.  The  markings 
given  in  his  drawings  can  be  traced  at  tlie  present  day,  and  are 
made  use  of  to  determine  the  exact  period  of  rotation  of  the  planet. 
So  well  is  the  rotation  fixed  by  them  that  the  astronomer  can  now 
determine  the  exact  number  of  times  the  planet  has  rotated  on  its 
axis  since  these  old  drawings  were  made.  The  period  has  been 
found  to  be  24^  87*  98* '7,  a  result  which  appears  certain  to  one  or 
two  tenths  of  a  second.'  It  is  therefore  leas  than  an  hour  greater 
than  the  period  of  roUttion  of  the  earth. 

•nfMS  ef  Xais. — ^Tbe  most  interesting  result  of  these  markings 
on  Man  is  the  proliabiUty  that  its  surface  is  diversified  by  land  and 
water,  covered  by  an  atmosphere,  and  altogether  very  shnilar  to  the 
surface  of  the  earth.  Some  portions  of  the  surface  are  of  a  dedded 
red  odor,  and  thus  give  rise  to  the  well-known  llery  aspect  of  the 
planet  Other  parts  are  of  a  greenish  hue,  and  are  therefore  top* 
poaed  to  be  seas.    The  most  striking  features  are  two  brilliant  white 


gftitiiMiii 


ihown  in  tho  fol- 


iinltcr  26tb. 
lary  81st. 
Bh6lh. 

met,  ariaing  from 
i  between  saoces- 
ine  month  to  two 

ay  are  not  lo  well 
I  the  hemisphere 
)  earth  is  always 
est  phase  occurs 
lie  son,  and  even 
,  like  that  of  the 
K>n.  The  phases 
0. 

■en  noticed  that  tha 
tnd  brightncsi,  but 
Hooks  found  that 
ed  around  in  nicli  a 
lit.  The  marliings 
resent  day,  and  are 
Ation  of  tlie  planet, 
istronomer  can  now 
I  lias  rotated  on  its 
le  period  baa  been 
ra  certain  to  one  or 
lan  an  hour  greater 

of  these  markinga 
ifsifled  by  land  and 

Tery  similar  to  the 
>oe  are  of  a  dedded 
I  llery  aspect  of  the 
3  are  therefore  sup- 
I  two  brilliant  white 


■>"tiaw 


TBS  PLANET  MARS. 


236 


regions,  one  lying  around  e»ch  pole  of  the  planet.  It  has  been  sup- 
posed  that  this  appearance  is  due  to  immense  masses  of  snow  and 
ice  surrounding  the  poles.  If  this  were  so,  it  would  indicate  that 
the  processes  of  evaporation,  cloud  formation,  and  condensation  of 
▼apor  into  rain  and  snow  go  on  at  ihe  surface  of  Man  as  at  the  sur- 
face of  the  earth.  A  certain  amount  of  color  is  giren  to  this  theory 
by  supposed  changes  in  the  magnitude  of  these  ice-caps.  But  the 
problem  of  establishing  such  changes  is  one  of  extreme  difficulty. 
The  only  way  in  which  an  adequate  idea  of  this  difficulty  can  be 
formed  is  by  the  student  himself  looking  at  Man  through  a  telescope. 
If  he  will  then  note  how  hard  it  is  to  make  out  the  different 
shades  of  light  and  darkness  on  the  pknet,  and  how  they  must  vary  in 
aspect  under  different  contlitions  of  clearness  in  our  own  atmosphere, 
he  will  readily  perceive  that  much  evidence  is  necessary  to  esUbiish 
great  changss.  All  we  can  say,  therefore,  is  that  the  formation  of 
the  ice-«api  in  winter  and  their  melting  in  summer  has  some  evi- 
dence in  its  favor,  but  is  not  yet  completely  proven. 

BAItUITU  OT  KiJM^ 

Until  the  year  1877  Man  was  supposed  to  have  no  satellites,  none 
having  ever  been  seen  in  the  most  powerful  telescopes.  But  in 
August  of  that  year  Professor  Hall,  of  the  Naval  Observatory. 
Instituted  a  systematic  search  with  the  great  equatorial,  which 
resulted  in  the  discovery  of  two  such  objects. 

These  satellites  are  Iqr  far  the  smallest  celestial  bodies  known.  It  is 
of  course  impossible  to  meaaure  their  diameters,  as  they  appear  in 
the  telescope  only  as  poinU  of  light  The  outer  satellite  is  probaUy 
about  tdx  miles  and  the  inner  one  about  seven  miles  in  diapeter. 
TIm  outer  one  was  seen  with  the  telescope  at  a  disUnce  from  the 
earOi  of  7,000,000  timea  this  diameter.  The  proportion  would  be 
that  of  a  ball  two  inches  in  dhuneter  viewed  at  a  distance  equal  to 
that  between  the  cities  of  Boston  and  New  York.  Such  a  feat  of 
telescopic  seeing  is  well  fitted  to  give  an  idea  of  the  power  of  modem 
optical  instruments. 

Professor  Hall  found  that  the  outer  satellite,  which  he  called 
JkimM,  nvolves  around  the  planet  in  80^  16",  and  the  inner  one, 
oiled  PMm,  in  T'  88".  The  ktter  ia  only  6800  jnilea  from  the 
centre  of  Jfori,  and  less  than  4000  miles  from  its  surface.  It  would 
therefore  be  almost  possible  with  one  of  our  telescopes  on  the  sur- 
ftoe  of  Man  to  see  an  object  the  aixe  of  a  hufge  animal  on  the 
■atellite. 

This  short  distance  and  rapid  revolution  make  the  inner  satellite 


m\ 


M 


AsmONOMt. 


of  Ibn  one  of  the  most  iolemting  bodies  with  which  wo  nre  «6 
qiwintt^l.  It  perfornu  ■  reTulution  iu  iu  orbit  iii  lew  ilwii  half  the 
time  that  Mar$  ravolTea  ou  iu  iizis.  Iu  couaequenco,  to  the  inbab- 
iuuts  of  Jfart  it  would  eeem  to  rise  iu  thu  went  aud  wt  iu  the  east. 
It  will  be  remembered  that  the  revolution  of  the  moon  around  tlM 
earth  and  of  the  earth  on  iu  aiia  are  both  from  weat  to  eaat;  bat  Um 


latter  rarolntlon  being  the  more  rapid,  the  apijarent  diurnal  motfon 
of  the  moon  is  from  east  to  west.  In  the  case  of  the  inner  satellite 
of  Man,  however,  this  is  reversed,  and  it  therefore  appeara  to  move 
in  the  actuiU  direction  of  its  orbiul  motion.  The  rapidity  of  ita 
phases  is  also  equally  remarkable.  It  is  less  than  two  hours  from 
■ew  moon  to  first  quarter,  and  no  on.  Thus  the  inhabitants  of  Man 
may  see  their  inner  moon  pass  through  all  iu  phases  from  new  to 
full  and  again  to  new  iu  a  single  night. 


wm&m 


wm 


IBstew* 


Ii  which  wo  nre  i^ 
II  IcM  ilwii  half  Um 
enc«,  to  Ui«  inhab* 
aud  wt  iu  the  vuL 
t  muon  ftruund  Uw 
real  to  eut;  bat  Um 


ntdiaml  motfoa 
the  inner  aatelllto 
e  appenra  to  moTe 
he  rapidity  of  ita 
I  two  hours  from 
ihabitanta  of  Jfora 
from  new  to 


CHAPTER  VI. 


THE  MINOR  PLANETS. 


Whbk  the  Boli*^  «v«tein  was  flrat  mapped  out  in  its  tnie 
proportions  by  Cv  .»j!^icu8  and  Kepler,  only  six  primary 
planets  were  known;  namely,  Mercury,  Venus,  the  Earth, 
Mara,  Jupiter,  and  Saturn.  These  succeeded  each  other 
according  to  a  nearly  regular  law,  as  we  have  shown  in 
Chapter  I.,  except  that  between  Mara  and  Jupiter  a  gap 
was  left  where  an  additional  planet  might  be  inserted, 
and  the  order  of  distances  be  thus  made  complete.  It  was 
therefore  supposed  by  the  astronomers  of  the  seventeenth 
«nd  eighteenth  centuries  that  a  planet  might  be  found  in 
this  region.  A  search  for  this  object  was  instituted  to- 
ward the  end  of  the  last  century,  but  before  it  had  mode 
much  progress  a  planet  in  the  place  of  the  one  so  long 
expected  was  found  by  Piazzi,  of  Palermo.  The  discov- 
ery was  made  on  the  first  day  of  the  present  century,  1801, 
January  1st. 

In  the  course  of  the  following  seven  years  the  astronom- 
ical world  was  surprised  by  the  discovery  of  three  other 
pUmets,  all  in  the  same  region,  though  not  revolving  in 
the  same  orbits.  Seeing  four  small  planets  where  one 
large  one  onght  to  be,  Olbbbs  was  led  to  his  celebrated 
hypothesis  that  these  bodies  were  the  fragments  of  a  large 
planet  which  had  been  broken  to  pieces  by  the  action  of 
lome  unknown  force. 


338 


ASTRONOMY. 


f 


A  generation  of  astronomers  now  passed  away  without 
the  discovery  of  more  than  these  fonr.  In  1845  a  fifth 
planet  of  the  group  was  found.  In  1847  three  more  were 
discorered,  and  discoveries  have  since  been  made  at  a  rate 
which  thus  far  shows  no  signs  of  diminution.  The  num- 
ber 1)08  now  reached  225,  and  the  discovery  of  additional 
ones  seems  to  be  going  on  as  fast  as  ever.  The  frequent 
announcements  of  tlie  discovery  of  planets  which  appear 
in  the  public  prints  all  refer  to  bodies  of  this  group. 

The  minor  planets  are  distinguished  from  the  major 
ones  by  many  characteristics.  Among  those  we  may  men- 
tion their  small  size;  their  positions,  all  being  situated  be- 
tween the  orbits  of  Mara  and  Jupiter;  the  great  eccentrici- 
ties and  inclinations  of  their  orbits. 

VamlMr  vf  Bautll  PUnato.— It  would  be  interesting  to  Icnow  how 
many  of  tlicse  planets  tlicre  are  in  all,  but  it  is  as  yet  imimssible  even 
to  guess  at  tlio  number.  As  already  stated,  fully  200  are  now 
known,  and  tlie  number  of  new  ones  found  every  year  ranges  from 
7  or  8  to  10  or  13.  If  ten  ndditional  ones  are  found  every  year  dur- 
ing the  remainder  of  tlie  century.  400  wUl  tlien  have  been  dis- 
covered. 

A  minor  planet  presents  no  sensible  disk,  and  therefore  looks  ex- 
actly like  a  small  star.  It  can  be  detected  only  by  its  motion  among 
the  surrounding  sUrs,  which  is  so  slow  that  hours  must  elapse  before 
it  can  be  noticed. 

Kagaltudss. — It  is  impossible  to  make  any  precise  measurement  of 
the  diameters  of  the  minor  planets.  These  can,  however,  be  esti- 
mated by  the  amount  of  lir'^t  which  the  planet  reflects.  Supposing 
the  proportion  of  light  reflected  about  the  same  as  in  the  case  of  the 
larger  planets,  it  is  estimated  that  the  diameters  of  the  three  or  four 
largest,  which  are  those  first  discovered,  range  between  800  and  600 
kilometres,  while  the  smallest  are  probably  from  20  to  60  kilometres 
in  diameter.  The  average  diameter  of  all  that  are  known  is  perhaps 
less  than  160  kilometres;  that  is,  scarcely  more  than  one  hundredth 
that  of  the  earth.  The  volumes  of  solid  bodies  vary  as  the  cubes  of 
their  diameters;  it  miglit  therefore  take  a  million  of  these  planets  to 
make  one  of  the  size  of  the  eiirili. 


/ 


id  Bwajr  without 
In  1845  a  fifth 
three  mor^  were 
)  mudo  at  a  rate 
on.  The  nnm- 
>ry  of  additional 
.  The  frequent 
ts  which  appear 
liis  group, 
from  the  major 
'se  we  may  men- 
sing  situated  be- 
great  eccentrici- 


ting  to  know  bow 
ret  in)|)088ible  even 
rully  aOO  nro  now 
f  year  ranges  from 
nd  every  year  dur- 
:n  bare  been  d<8> 

herefore  looka  ex- 
T  its  motion  among 
must  elapse  before 

ise  measurement  of 
,  bowevor,  be  esti- 
tflects.  Supposing 
in  tbe  case  of  tbe 
f  tbe  tbree  or  four 
tween  800  and  600 
!0  to  60  kilometres 
)  known  is  perbaps 
lan  one  bundredtb 
iry  as  tbe  cubes  of 
[>f  tbese  planets  to 


THE  MINOR  PLANETS. 


330 


loTB  «f  Orbits.— Tlie  orbits  of  tbe  minor  planets  are  mucb  more 
ecct  uric  Ibaii  those  of  tbe  larger  ones;  tbeir  distance  from  tbe  sun 
tbercforo  varies  very  widely. 

Orifia  sf  the  Viaer  naaeU.— The  question  of  tbe  origin  of  tbese 
bodies  was  long  one  of  great  interest.  The  features  which  we  have 
described  ttssociute  themselves  very  naturally  wltli  the  bypotbesis 
of  Olbkrs,  that  wc  here  have  the  fragmenU  of  a  single  large  planet 
which  in  tbe  beginning  revolved  In  iU  proper  place  between  tbe 
orbits  of  Mar$  and  Jupiter.  No  support  has  been  given  to  Olbcbs' 
bypotbesis  by  subsequent  investigations,  and  it  is  no  longer  consid- 
ered by  astronomers  to  have  any  foundation.  So  far  as  can  be  Judged, 
tbese  bodies  have  been  revolving  around  tbe  sun  as  separate  planett 
ever  since  the  solur  system  itself  was  formed. 


•"'"'V-^^^'v 


L. 


CHAPTER  VII. 
JUPITER  AND  HIS  SATELLITES. 

TBI  FiAvn  JumsB. 

Jupiter  is  much  the  largest  planet  in  the  system.  His 
mean  distance  is  nearly  800,000,000  kilometres  (480,000,- 
000  miles).  His  diameter  is  140,000  kilometres,  corre- 
sponding to  a  mean  apparent  diameter,  as  seen  from  the 
snn,  of  30'. 5.  His  linear  diameter  is  about  ■^,  his  surface 
is  T^,  and  his  volume  t^itt  th»t  o'  the  snn.  His  mass  is 
T-rfrr,  and  his  density  is  thus  nearly  the  same  as  the  sun's; 
vit.,  0.24  of  the  earth's.  He  rotates  on  his  axis  in 
9"  SS"  20*. 

He  is  attended  by  four  satellites,  which  were  discorered 
by  Galileo  on  January  7th,  1610.  He  named  them,  in 
honor  of  tlie  Medicis,  the  Medicean  stars.  They  are 
now  known  as  Satellites  I,  II,  III^  and  IV,  I  being  the 
nearest. 

The  surface  of  Jupiter  has  been  carefully  studied  with 
the  telescope,  particularly  within  the  past  twenty  years. 
Although  further  from  us  than  Mars,  the  details  of  his 
disk  are  much  easier  to  recognize.  The  most  characteristic 
features  are  given  in  the  drawings  appended.  These 
featui-cs  are,  first,  the  dark  bands  of  the  equatorial 
regions,  and,  secondly,  the  cloud-like  forms  spread  over 
nearly  the  whole  surface.  At  the  limb  all  these  details 
become  indistinct,  »nd  finally  vanishi  %\vw  indicftting  « 


DiHMii 


JVPITBB  AXD  HIS  BATELUTBB. 


HL 


"ES. 


te  system.  His 
stres  (480,000,- 
ometres,  oorro* 
seen  from  the 
;  ^,  his  surface 
His  mass  is 
le  as  the  sun's; 
I   his    axis    in 

irere  discovered 
inmed  them,  in 
tr».  They  are 
V,  I  being  the 

iy  studied  with 
twenty  years. 
I  details  of  his 
t  characteristic 
•ended.  These 
the  equatorial 
18  spread  oyer 
1  these  details 
8  indicating  « 


highly  absorptive  atmosphere.  The  light  from  the  centre 
of  the  disk  is  twice  as  bright  as  that  from  the  poles.  The 
bands  can  be  seen  with  instruments  no  more  |)owcrful 
than  those  used  by  GAUiiio,  yet  he  makes  no  mention  of 
them. 

The  color  of  the  bands  is  reddish.  The  position  of  the 
bands  varies  in  latitude,  and  the  shapes  of  the  limiting 
curves  also  change  from  day  to  day;  but  in  the  main  tliey 
remain  as  permanent  features  of  the  region  to  which  they 
belong.    Two  such  bands  are  aanally  vimble,  but  often 


f^TL— ' 


▼iDnr  ov  Svramktm  mm  a*TBums. 


more  are  seen.  Hkbmhbl,  in  the  year  1798,  attributed 
the  aspects  of  the  bands  to  zones  of  the  phinet's  atmos- 
phere more  tranquil  and  less  filled  with  clouds  than  the  re- 
maining portions,  so  as  to  permit  the  true  surface  of  the 
planet  to  be  seen  through  these  zones,  while  the  prevailing 
clouds  in  the  other  regions  give  a  brighter  tint  to  these 
latter.  The  color  of  the  bands  seems  to  vary  from  time  to 
time,  and  their  bordering  lines  sometimes  alter  with  such 
rapidity  as  to  show  that  these  borders  are  formed  of  some- 
thing like  clouds. 
Tho  olon<|§  ^l^pmeelv^  ^j^  ^ily  be  aeen  at  times,  and 


L 


ASTRONOMY. 


I 


lib 


thoy  liave  every  variety  of  abupe,  aometimos  appearing  ai 
brilliant  circular  wbite  masses,  but  oftonor  thoy  are  similar 
in  form  to  a  aeries  of  white  cumulus  clouds  such  as  arc 
frequently  seen  piled  up  near  the  horizon  on  a  summer's 
day.  The  bands  themselves  seem  frequently  to  be  veiled 
over  with  something  like  the  thin  cirrus  clouds  of  our  at- 
mosphere. 


Vm.  71.— TauMoono 


Vww  or  Jtmnn, 

Hm  OM  no 


wm  A  SAnum  um  m  Ibabow 


Bueh  olouds  can  be  tolerably  socurstely  observed,  and  may  be  used 
to  determine  the  rotatloa-time  of  the  planet.  Tlieae  obaervations 
show  that  the  clouds  have  often  a  motion  of  their  owb,  which  is  also 
evident  from  other  oondderatlons. 

The  following  results  of  observation  of  spots  situated  in  various 
ngions  of  the  planet  will  illustrate  this: 


(108  appearing  ai 
r  thoy  are  similar 
)udB  Buoh  ai  aro 
k  on  a  Bummor'a 
intly  to  be  Teilod 
olouda  of  oar  at- 


JVI'JTElt  AXD  UIS  HATKILITA'S. 


Oamini 166S, 

Hbrkrki. 1778, 

HUIKBRL 1779. 

SCHROKTRB. 1788, 

Bub  and  MIdlcr  .  1885, 

AiBT 1888, 

soHMioT Idea, 


M8 


A* 

w. 

f. 

rotation-time 

=  9 

M 

00 

=  9 

08 

40 

s:  9 

60 

48 

=  9 

06 

CO 

s:  9 

55 

20 

=  9 

68 

81 

ta  9 

S6 

M 

lARB  iin  m  tmjkBom 


ed,  and  nuy  be  med 
TImm  obflerrationa 
r  own,  which  ia  alao 

situated  in  ▼arioua 


Thi  (Unuini  or  Jtrnm. 

■•tima  af  thr  *r>ti!'Utas.— Tlie  four  satellites  more  about  Jvpttm> 
from  weat  to  eatt  a  nearly  circular  orbits.  When  one  of  these 
satellflea  passes  between  the  sun  and  Jupittr,  it  casts  a  shadow  upon 
fvfit»t't  disk  (Me  Fig,  78)  precisely  as  the  shadow  of  our  moon  is 


^lit' 


\i 


rni;  . 


944 


ASTRONOMY. 


thrown  upon  the  earth  in  a  solar  eclipse.  If  the  gatellUe  passes 
through  Jupiter't  own  shadow  in  its  revolution,  nn  eclipse  of  this 
satellite  takes  place.  If  it  passes  between  the  earth  and  Jupiter,  it 
is  projected  upon  Jupiter's  disk,  and  we  liave  a  transit;  if  Jupiter  is 
between  the  earth  and  the  satellite,  an  occultatlon  of  the  latter  oc- 
curs. All  these  phenomena  can  be  seen  with  a  common  telescope, 
and  the  times  of  observation  are  all  found  predicted  in  the  Nautical 
Almnnae.  These  shadows  being  seen  black  upon  Jupiter't  surface, 
show  timt  tills  planet  shines  by  reflecting  the  light  of  the  sun. 

Teleseopie  Appaaranea  «f  the  lateUitM.— Under  ordinary  circum- 
stances, the  satellites  of  Jupiter  axe  seen  to  have  disks;  that  is,  not 
to  be  mere  points  of  light.  Under  very  favorable  conditions,  mark- 
ings have  been  seen  on  these  disks. 

The  salellites  completely  disappear  from  telescopic  view  when 
they  enter  the  shadt  w  of  the  planet.  This  seems  to  show  that 
neither  planet  nor  satellite  is  self-luminous  to  any  great  extent.  If 
the  satellite  were  self-luminous,  it  would  be  seen  by  its  own  light; 
and  if  the  planet  were  luminous,  the  satellite  might  be  seen  by  the  re- 
flected light  of  the  planet. 

The  motions  of  these  objects  are  connected  by  two  curious  and 
iiuporunt  relations  discovered  by  La  Place,  and  expressed  as  fol- 
lows: 

I.  37m  mean  motion  of  (he  fint  eatOUte  added  to  twice  the  mean  mo- 
tion of  the  Oiird  it  exaetty  equal  to  three  timet  the  mean  motion  of  the 
leeoiid. 

II.  ^  to  the  mean  longitude  ef  the  fret  tateKte  tM  add  twice  the  mean 
longitude  of  the  third,  and  tubtraet  (Arse  timet  the  mean  longitude  if  the 
eteond,  the  difference  it  alreayt  180°. 

The  fint  of  these  relations  is  shown  in  the  following  table  of  the 
mean  daily  motions  of  the  satellites: 

Satellite  I  hi  one  day  moTM. 2(IS*.48W 

«•      n     "           "         lOr.8748 

"     III     ••           "          60°.8177 

•«     IV     "           "         ai'.STll 

Motion  of  Satellite  1 808°.48»0 

Twice  that  of  Satellite  m 100°.6854 

Sum 804M844 

Three  times  motion  of  SatelUte  TL 804MaM 

Observations  showed  tliat  this  condition  was  fulfilled  as  exactly  «■ 
possible,  but  the  discovery  of  La  Plack  consisted  in  showing  that  if 
the  approximate  coincidence  of  the  mean  motions  was  opce  ettftb- 


;  the  satellite  passes 
D,  nn  eclipse  of  this 
earth  and  Jupiter,  it 
transit;  if  Jupiter  is 
ion  of  the  latter  oc- 
I  common  telescope, 
licted  in  the  NdutietU 
K)n  Jupiter's  surface, 
;ht  of  the  sun. 
ler  ordinary  circum- 
ve  disks;  that  is,  not 
ble  conditions,  mark- 

elescopic  view  when 
seems  to  show  that 
any  great  extent.  If 
!en  by  its  own  light; 
ight  be  seen  by  the  re- 

by  two  curious  and 
ind  expressed  as  fol- 

to  twiee  the  mean  mo- 
he  mean  motion  ef  ih» 

tM  add  titiee  the  mean 
I  mean  longitude  <if  the 

(ollowing  table  of  the 

...  2(»*.48M 
...  ior.8748 
...      60°.8m 

....    ar.6711 

....    S08°.48B0 
....    100°.6854 


804M844 
804MaM 


fulfllled  as  exactly  ai 
ited  in  showing  that  if 
•tions  was  opce  eatftb- 


JUPITEB  AND  HIS  BATELLITE8. 


34ff 


lished,  they  could  never  deviate  from  exact  coincidence  with  the 
law.  The  case  is  analogous  to  that  of  the  moon,  which  always 
presents  the  same  face  to  us  and  which  always  will,  since  the  rela- 
tion being  once  approximately  true,  it  will  become  exact  and  ever 
remain  so. 

Tlie  discovery  of  the  gradual  propagation  of  light  by  means  of 
these  satellites  has  already  been  described,  and  it  has  also  been  ex- 
plained that  tlicy  are  of  use  in  the  rough  determination  of  longi- 
tudes. To  facilitate  their  observation,  the  Nautical  Almanac  gives 
complete  epbemerides  of  tlielr  phenomena.  A  specimen  of  a  portion 
of  such  an  ephemcris  for  1865,  March  7th,  8th,  and  9th,  is  added. 
The  times  are  Washington  mean  times. 

1865— March. 


d,    h,    m.      $. 

I 

Eclipse 

Disapp. 

7    18    27    88.5 

I 

Occult. 

Reapp. 

7    21    66 

III 

Shadow 

Ingress 

8      7    27 

III 

Shadow 

Egress 

8     9    68 

III 

Transit 

Ingress 

8    12    81 

II 

Eclipse 

Disapp. 

8    18     1    22.7 

III 

Transit 

Egress 

8    16     6 

II 

Eclipse 

Beapp. 

8    15    24    11.1 

n 

Occult. 

Disapp. 

8    15    27 

I 

Shadow 

Ingress 

8    15    48 

I 

Transit 

Ingress 

8    16    58 

I 

Shadow 

Egress 

8    17    67 

II 

Occult. 

Reapp. 

8    17    69 

I 

Transit 

Egress 

8    19    18 

I 

Eclipse 

Disapp. 

9    12    65    59.4 

I 

Occult. 

Reapp. 

9    16    26 

Suppose  an  observer  near  New  York  City  lo  have  determined  his 
local  time  accurately.  Tliis  is  about  18<*  faster  than  Washington 
time.  On  1865.  March  8th,  lie  wonlil  K)ok  for  the  reappearance  of 
II  at  about  15'*  84"  of  liia  local  time.  Suppose  he  observed  it  at 
15^  36-  22'.7  of  his  time:  then  his  meridian  is  12-  11'.6  east  of 
Washington.  The  difficulty  of  observing  these  eclipses  with  acca- 
racy,  and  the  fact  that  the  nperturs  of  the  telescope  employed  has  an 
Important  effect  on  the  appearances  seen,  have  kept  this  method 
from  a  wide  utility,  which  it  at  first  seemed  to  promise. 


---'i3i  tifc*;.«^Kt.v>c«-- . 


iv,--:4***WWi^''w-'= 


\  ! 


¥ 


CHAPTER  VIII. 
BATUKSr  AND  ITS  SYSTEM. 

OxvxBAL  Dnoumov. 

Saturn  is  the  most  distant  of  the  major  planets  known 
to  the  ancients.  It  revolves  around  the  sun  in  29^  years, 
at  a  mean  distance  of  about  1,400,000,000  kilometres 
(882,000,000  miles).  The  angular  diameter  of  the  ball  of 
the  planet  is  about  16'.  2,  corresponding  to  a  true  diameter 
of  about  110,000  kilometres  (70,600  miles).  Its  diameter 
is  therefore  nearly  nine  times  and  its  volume  about  700 
times  that  of  the  earth.  It  is  remarkable  for  its  small 
density,  which,  so  far  as  known,  is  less  than  that  of  any 
other  heavenly  body,  and  even  less  than  that  of  water.  It 
revolves  on  its  axis  in  10"  14'°  24%  or  less  than  half  a  day. 

Saturn  is  perhaps  the  most  remarkable  planet  in  the 
solar  system,  being  itself  the  centre  of  a  system  of  its 
own,  altogether  unlike  anything  else  in  the  heavens.  Its 
most  noteworthy  featuie  is  a  pair  of  rings  which  surround 
it  at  a  considerable  distance  from  the  planet  itself.  Out- 
side of  these  rings  revolve  no  less  than  eight  satellites, 
or  twice  the  greatest  number  known  to  surround  any  other 
planet.  The  planet,  rings,  and  satellites  are  altogether 
called  the  Saturnian  system.  The  general  appeannoe  of 
this  system,  as  seen  in  a  small  telescope,  is  shown  in  Fig.  74. 


BATURN  AND  ITS  ST8TEM. 


947 


•r  planets  known 
sun  in  29^  years, 
),000  kilometres 
ter  of  the  ball  of 
>  a  true  diameter 
s).  Its  diameter 
>lume  about  700 
)le  for  its  small 
than  that  of  any 
bat  of  water.  It 
than  half  a  day. 
le  planet  in  the 
a  system  of  its 
the  heavens.  Its 
a  which  surround 
met  itself.  Out- 
eight  satellites, 
irround  any  other 
es  are  altogether 
ral  appeannoeof 
shown  in  Fig.  74. 


To  the  naked  eye  Saturn  is  of  a  dull  yellowish  color, 
shining  with  about  the  brilliancy  of  a  star  of  the  first  mag- 
nitude. It  varies  in  brightness,  however,  with  the  way  in 
which  its  ring  is  seen,  being  brighter  the  wider  the  ring 
appears.  It  comes  into  opposition  at  intervals  of  one  year 
and  from  twelve  to  fourteen  days.    The  following  are  the 


Ito.  74.— TtaaKiono  Yaw  or  nn  SAumtoAK  Bnrmt. 

times  of  some  of  these  oppositions,  by  studying  which  one 
will  be  enabled  to  recognize  the  planet: 

1882 November  14th. 

1883 November  28th. 

1884. December  11th. 

During  these  years  it  will  be  best  seen  in  the  autumn 
and  winter. 

When  viewed  with  a  telescope,  the  physical  appearance 
of  the  ball  of  Saturn  is  quite  similar  to  that  of  JuinUr, 


1^ 


AsmoyoAfT. 


(^ 


li 


■a 


having  light  and  dark  belts  parallel  to  the  direction  of  its 
rotation. 

Tes  Rnrcn  or  SATinur. 

TLe  rings  are  the  most  wmarkablo  and  characteristic  feature  of 
tile  Saturiiian  system.  Pig.  75  gives  two  views  of  tbe  ball  and  rings. 
The  upper  one  shows  one  of  their  aspects  as  actually  presented  in 
tlie  telescope,  and  the  lower  one  shows  what  the  appearance  would 
be  if  the  planet  were  viewed  from  a  direction  at  right  angles  to  the 
plane  of  the  ring  (wliich  it  never  can  be  from  tbe  earth). 

The  first  telescopic  observers  of  Hilurn  were  unable  to  see  the 
rings  in  their  true  form,  and  were  greatly  perplexed  to  account 
for  the  appearance  wliicli  the  planet  preM.>nted.  Oami.eo  descrilied 
the  planet  as  "  trl-corporale,"  the  two  ends  of  the  ring  having,  in  his 
imperfect  telescope,  the  appearance  of  a  pair  of  small  pluneU  at- 
tached to  the  central  one.  "On  eacli  side  of  old  Utturn  were  ser- 
vitors who  aided  liim  on  his  way."  This  supposed  discovery  was 
announced  to  his  friend  Kbplkb  in  this  logogriph : 

"smaismrmilmepoetalcTmibuncnugltsviras,"  which,  being  trans- 
posed, becomes — 

"Aitissimum  planetam  tergeminum  observavi"  (I  liave  observed 
the  most  distant  planet  to  be  tri-form). 

The  phenomenon  constantly  remained  a  mystery  lo  iU  first  ob- 
server. In  1910  lie  had  seen  the  planet  accompanied,  as  he  supposed, 
by  two  lateral  stars;  in  1012  the  latter  had  vanished  and  the  central 
body  alone  remained.    After  that  Oalilbo  ceased  to  observe  Satitm. 

The  appearances  of  the  ring  were  also  incomprehensible  to  Hb- 
VBLitJS.  GAssBNDt,  and  othera.  It  was  not  until  lOSS  (after  seven 
yeara  of  observation)  that  the  celebrated  Hctghers  discovered  the 
true  explanation  of  tbe  remarkable  and  recurring  series  of  phenom- 
ena present  by  tiie  tri-corporate  planet. 

He  announced  his  conclusions  in  the  following  logogriph: 

"aaaaaa  ccccc  d  eeeee  g  h  iiiiiii  1111  mm  nnnnonnnn  oooo  pp  q  rr  a 
ttttt  uuuuu,"  which,  when  arranged,  read— 

"  Annulo  cingitur,  tonui,  piano,  nusquam  coherente,  ad  eclipticam 
inclinato"  (it  is  girdled  by  a  Uiir  plane  ring,  nowhere  touchinir  in- 
clined  to  the  ecliptic).  *'       , 

Thia  description  is  complete  and  accurate. 

In  1676  it  was  found  by  Cassihi,  tliat  what  HmroBJora  had  seen 
as  a  single  ring  was  really  two.  A  division  extended  all  the  way 
aroand  near  tbe  outer  edge.    This  division  is  shown  in  tlie  flguns 

In  18SQ  the  Vmm.  Bokd.  of  Harvard  College  Observatory.  fMiad 


direction  of  its 


iteristic  feature  of 
the  ball  and  rings. 
:ually  presented  in 
appearance  would 
-ight  angles  to  the 
arth). 

unable  to  see  the 
ilcxed  to  account 
}ami.bo  descrilted 
ring  having,  in  his 
small  planets  at- 
I  Untune  were  ser- 
sed  discovery  was 

lich,  being  trans- 

(I  have  observed 

ry  to  ite  first  ob- 
d.  as  lie  supposed, 
id  and  the  central 
to  observe  Saturn. 
rehensiblo  to  Hr- 
1095  (after  seven 
HB  discovered  the 
series  of  phenom- 

•gogriph: 

nn  oooo  pp  q  rr  s 

ite,  ad  eclipticam 
iicre  touching,  in- 


roBKJra  had  seen 
ided  all  the  waj 
1  in  the  flguns. 
Mervatoiy,  fomd 


l-lfeSiS;-- 


/ 


Jl 


I 

'  t     St 


1^ 


ASTRONOMf. 


that  then  wu  a  third  ring,  of  a  dusky  and  nebulous  aspect,  inside  the 

other  two,  or  rather  attached  to  the  inner  edge  of  the  inner  ring     It 

is  therefore  known  as  Bwwf «  duiky  ring.    It  hud  not  been  before  fully 

described  owing  to  its  darkness  of  color,  which  made  it  a  difBcult 
object  to  see  except  witli  a  good  telescope.  It  is  not  separated  from 
the  bright  ring,  but  seems  as  if  attached  to  It.  The  latter  shades  off 
toward  iu  inner  edge,  and  merges  gradually  into  the  dusky  ring. 
The  latter  extends  about  half  way  from  the  inner  edge  of  the  bricht 
ring  to  the  ball  of  the  planet 

Aspeet  of  the  Blogi.— As  Saturn  revolves  around  the  lun,  the 
plane  of  the  rings  remains  parallel  to  itself.  That  is,  if  we  consider 
a  straight  line  passing  through  the  centre  of  the  planet,  perpendic- 
ular to  the  plane  of  the  ring,  as  the  axis  of  the  latter,  this  axis  will 
Mways  point  in  the  same  direction.  In  this  respect  the  motion  is 
similar  to  that  of  the  earth  around  the  sun.  The  ring  of  Saturn  is 
inclined  about  ST  to  the  plane  of  its  orbit.  Consequently,  as  the 
planet  molTaa  around  the  sun.  there  is  a  change  in  the  diiecUon  in 
Which  the  nm  ehines  upon  it  similar  to  that  which  produces  the 
change  of  seaeona  upon  the  earth,  as  shown  in  Pig.  82. 

The  oarreiponding  changes  for  Saturn  are  shown  in  Fig  76  Dur- 
ing each  revolution  of  Saturn  \.Ub  plane  of  the  ring  passes  through 
the  sun  twice.  This  occurred  in  the  years  1862  and  1878.  at  two 
oppoeite  points  of  the  orUt.  us  shown  in  the  figure.  At  two  other 
points,  midway  between  these,  the  sun  shines  upon  the  plane  of  the 
ring  at  ito  greatest  incUnatioa.  about  27°.  Since  the  earth  is  Jinle 
more  thaa  one  tenth  aa  far  from  the  sun  as  Saturn  is.  an  obwsrver 
^ways  sf«8  Saturn  nearly,  but  not  quite,  as  if  he  were  upon  the  sun 
Hence  at,  certain  times  the  rings  of  Saturn  are  seen  edgeways;  while 
at  otiier  times  they  are  at  an  inclination  of  27°,  the  aspect  depending 
upon  the  position  of  the  planet  in  ito  orbit.  The  followlng\re  Uio 
times  of  some  of  the  phases: 

1878.  Pebraaiy  7th.-The  edge  of  the  ring  was  turned  toward  tiie 
sun.    It  could  then  be  seen  only  as  a  thin  line  of  light 

1886.-The  planet  having  moved  forward  90°,  the  souUi  side  of  tiie 
rings  may  be  seen  at  an  inclination  of  27°. 

IWl,  Deoember.-The  planet  having  moved  90°  further,  tiie  edge 
of  the  ring  is  again  turned  toward  tiie  sun. 

1809.— The  north  side  of  the  ring  is  Inclined  toward  tiie  sun.  and 
is  seen  at  iu  greatest  inclination.  »».  "w 

The  rings  are  extremely  thin  in  proportion  to  tiieir  extent  Oon' 
sequently,  when  tiieir  edges  are  turned  toward  theeartii,  tiiey  aDma^ 
as  a  tiiin  line  of  light,  which  can  be  seen  only  witii  wiwerful  Sk 
•cope*     With  such  telewsopes.  tiie  planet  appeara  as  if  it  w«k 


SATUBN  AND  ITS  STSTBM. 


261 


lous  aspect,  in8ideth« 
>r  the  inner  ring.  It 
not  been  before  fully 
:b  made  it  a  difficult 
•  not  separated  from 
The  latter  shades  off 
into  the  dusky  ring. 
ler  edge  of  the  bright 

iround  the  sun,  the 
liat  is,  if  we  consider 
le  planet,  perpendic- 
I  latter,  this  axis  will 
espect  the  motion  is 
he  ring  of  Saturn  is 
Consequently,  as  the 
;e  in  the  direction  in 
which  produces  the 
ig.  83. 

wn  in  Fig  76.  Dor- 
ring  passes  through 
13  and  1878,  at  two 
ure.  At  two  other 
on  the  plane  of  the 
»  the  earth  is  JlUle 
urn  is,  an  obserror 
were  upon  the  sun. 
en  edgeways;  while 
lie  aspect  depending 
e  following  are  the 

3  turned  toward  the 

light 

lie  south  side  of  the 

0°  further,  the  edge 

iward  the  sun,  $3aA 

their  extent  Oon^ 
3  earth,  tfaey  appear 
rith  powerful  tele^ 
tears  as  if  it  w«i« 


pierced  through  by  n  piece  of  very  fine  wire,  the  ends  of  which  pro- 
ject on  each  side  more  than  the  diameter  of  the  planet.  It  has  fre- 
quently been  remarked  that  this  appearance  is  seen  on  one  side  of 
the  planet,  when  no  trace  of  the  ring  can  be  seen  on  the  other. 

There  is  sometimes  a  period  of  a  few  weeks  during  which  the 
plane  of  the  ring,  extended  outward,  passes  between  the  sun  and  the 
earth.  Tiiat  is,  the  sun  shines  on  one  side  of  the  ring,  while  the 
other  or  dark  side  is  turned  toward  the  earth.  In  this  case  it  seems 
to  be  established  that  only  the  edge  of  the  ring  is  visible.    If  this  be 


so,  the  substance  of  the  rings  cannot  be  transparent  to  the  sun's  rays, 
else  it  would  be  seen  by  the  light  which  passes  through  it 

Ceastitutien  *t  tIpevBiats  vt  latan'.— The  nature  of  these  objects 
ha»  been  a  subject '&>th.bf  wonder  and  of  investigation  by  mathema- 
ticians and  astronomers  ever  since  they  were  discovered.  They  were 
at  first  supposed  to  be  solid  bodies;  indeed,  from  their  appearance  it 
was  difficult  to  copceive  of  them  as  anything  else.  The  question 
Uien  arose:  What  keeps  them  from  falling  on  the  planet?  It  was 
shown  by  La  Placb  that  a  homogeneous  and  solid  ring  surroundbig 
the  planet  could  not  remain  in  a  state  of  equilibrium,  bat  must  be 
pncipltated  upon  the  central  ball  by  the  smallest  disturbing  force. 


AarnoNOMT. 


I 


M 


It  ia  now  establiMhed  beyond  reasonable  doubt  tbnt  the  ringa  do  not 
form  a  continuous  mass,  but  are  rtiilly  a  countluss  multitude  of  small 
separate  particles,  each  of  which  revolves  on  ito  own  account.  These 
sutullites  are  individually  far  too  small  to  be  seen  in  ony  teleKope.  but 
so  numeroua  that  when  viewed  from  the  distance  of  the  earth  they 
appear  aa  a  continuous  mass,  like  particles  of  dust  floating  in  a 
sunbeam. 

1 

SATUXITES  OV  BAtDBV. 

Outside  the  rings  of  Saturn  revolve  iu  eight  satellites,  the  order 
and  discovery  of  which  are  siiown  in  the  following  table: 


Dtstaaoe 

Mo. 

Nami. 

from 
PUuiet. 

DiacoTerer. 

Data  of  DlacoTery. 

1 

Mimas 

8-3 

Herscliel 

1789.  September  17. 

2 

Encelodus 

4-8 

Herscliel 

178d,  August  28. 

tf 

Tethys 

5.:i 

Ciifisini 

1684.  March. 

4 

Dione 

0-8 

Cassini 

1684,  March. 

ft 

Rhea 

0-5 

Cassini 

1«72,  December  28. 

0 

7 

Titan 
Hyperion 

20-7 
20-8 

Huyshens 

16S5,  March  25. 
1848,  September  16. 

8 

Japetus 

64-4 

Cassini 

1671,  October. 

The  distances  from  the  planet  are  given  in  radii  of  the  latter.  The 
satellites  Mimat  and  Hyperion  are  visible  only  in  the  moat  powerful 
teleM»pea.  The  brightest  of  all  ia  Titan,  which  can  be  seen  in  a 
teleacope  of  the  snialle«t  ordinary  size.  Japettu  has  the  remarkable 
peculiarity  of  apptoring  nearly  as  bright  as  lOan  when  seen  west  of 
the  planet,  and  so  faint  as  to  be  visible  only  in  large  telescopes  when 
on  the  other  side.  This  appearance  is  explained  by  supposing  that, 
like  our  moon,  it  always  preaenta  the  same  face  to  the  planet,  and 
that  one  side  of  it  is  dark  and  tlie  other  side  light.  When  west  of 
the  planet,  the  bright  side  is  turned  toward  the  earth  and  the  satel- 
lite ia  visible.  On  the  other  aide  of  the  planet,  the  dark  side  ia  turned 
toward  ua,  and  it  ia  nearly  invisible.  Most  of  the  remaining  five 
aateiiites  can  ordinarily  be  seen  with  teleacopes  of  moderate  power. 


that  the  ringa  do  not 
H  multitude  of  amiill 
iwD  account.  These 
in  any  telescope,  but 
:e  of  the  earth  they 
I  dust  floating  in  a 


satellites,  the  order 
ng  table: 


Data  of  DlscoTery. 


1789.  September  17. 
t78d,  Augustas. 
1684.  March. 
1684,  Miiich. 
L«7a,  December  28. 
t«S5,  Marches. 
1848,  September  10. 
1871,  October. 


11  of  the  latter.  The 
the  moat  powerful 
li  can  be  seen  in  a 
has  the  remarkable 
k  when  seen  west  of 
rge  telescopes  when 
by  supposing  thut, 
e  to  the  planet,  and 
ht.  When  west  of 
earth  and  the  satel- 
dark  side  is  turned 
the  remaining  five 
[  moderate  power. 


CHAPTER  IX. 
THE  PLANET  URANUS. 

Uranus  was  discovered  on  Murch  13lli,  1781,  by  Sir 
William  Herscuel  (then  an  amateur  observer)  with  a 
ten-foot  reflector  made  by  himself.  He  was  examining  a 
portion  of  the  sky  near  H  Oeminorum,  wlien  one  of  the 
otufs  in  the  field  of  view  attracted  his  notice  by  its  ])eculiur 
appearance.  On  further  scrutiny,  it  proved  to  ]iave  a 
planetary  disk,  and  a  motion  of  over  2'  per  liour.  Heuschel 
at  first  supposed  it  to  be  a  comet  in  a  distant  part  of  its 
orbit,  and  under  this  impression  parabolic  orbits  were  com- 
puted for  it  by  various  mathematicians.  None  of  these, 
however,  satisfied  subsequent  observations,  and  it  was 
finally  determined  that  the  now  body  was  a  planet  revolv- 
ing in  a  nearly  circular  orbit.  We  can  scarcely  compre- 
hend now  the  enthusiasm  with  which  this  discovery  Avas 
received.  No  new  body  (save  comets)  had  been  added  to 
the  solar  system  since  the  discovery  of  the  third  satellite 
of  Saturn  in  1684,  and  all  the  major  planets  of  the  heavens 
had  been  known  for  thousands  of  years. 

Uranus  revolves  about  the  snn  in  84  years.  Its  apparent 
diameter  as  seen  from  the  earth  vai'ies  little,  being  about 
3'.  9.  Its  true  diameter  is  about  50,000  kilometres,  and  its 
figure  is,  so  far  as  we  know,  exactly  spherical. 

In  physical  appearance  it  is  a  small  greenish  disk  with- 


d64 


AsrnoKoMr. 


M 


out  markings.  It  is  possible  tliat  the  centre  of  the  disk  is 
slightly  brighter  tiiun  the  edges.  At  its  nearest  approach 
to  the  earth,  it  Khines  us  a  star  of  the  sixtli  magnitude, 
and  is  just  visible  to  an  acute  eye  when  the  attention  is 
directed  to  its  place.  In  small  telescopes  with  low  powers, 
its  appearance  is  not  markedly  diflFerant  from  that  of  stars 
of  about  its  own  brilliancy. 

Sir  William  IIerscuel  suspected  that  Uranus  was  ac- 
companied by  six  ButuUites. 

Of  the  existence  of  two  of  those  satellites  there  has  never 
been  any  doubt.  None  of  the  other  four  satellites  de- 
scribed by  Uersciiel  lias  ever  been  seen,  and  he  was 
undoubtedly  mistaken  in  supposing  them  to  exist.  Two 
ailditional  ones  voro  discovered  by  Lasskll  in  1847,  and 
they  are,  with  the  Hatollites  of  Mara,  the  faintest  objects  in 
the  solar  system.  Neither  of  them  is  identical  with  any  of 
the  missing  ones  of  Herschel.  As  Sir  William  Her- 
8CHEL  had  susi^ected  six  satellites,  the  following  names  for 
the  true  satellites  are  generally  adopted  to  avoid  confusion: 

Dikn. 

I.   Arul , Period=    2.620888 

II.    Uti^rid "      =    4.144181 

III.  Titania,  Herscuel'b  (II.) "       -    8.708897 

IV.  06«w».  Hkbschei/s  (IV.) "      =18.463269 

It  is  likely  that  .^m/  -...ries  in' brightness  on  different 
sides  of  the  planet,  and  the  same  phenomenon  has  also 
been  suspected  for  Titania. 

The  most  remarkable  feature  of  the  satellites  of  Uranui  is  that 
their  orbits  are  uearly  perpendicular  to  the  ecliptic  instead  of 
having  a  small  inclinstioii  to  that  plane,  like  those  of  all  the  orbits 
of  both  planets  and  satellites  previously  known.  To  form  a  correct 
idea  of  the  position  of  the  orbits,  we  must  imagine  them  tipped  over 
until  their  north  pole  is  nearly  8°  below  the  ecliptic,  instead  of  80° 


:'J>'?S)#S 


«l3l 


centre  of  the  disk  is 
ts  nearest  approach 
e  sixth  magnitude, 
len  tlio  attention  is 
es  witli  low  powers, 
;  from  that  of  stars 

liat  Uranus  was  ac> 

lites  thoro  Ims  never 

four  satellites  de- 

seen,  and  he  was 

>em  to  exist.    Two 

lSSELL  in  1847,  and 

0  faintest  ohjects  in 

lentical  with  any  of 

Sir  William  Heb- 

fuUowing  names  for 

to  avoid  confusion: 

...Period  =  2.520888 
...  •'  =  4.144181 
...  "  ~  8.705897 
...  "   =18.463269 

;htnes8  on  different 
enomenon  has  also 


lites  of  Uranut  is  that 
he  ecliptic  instead  of 
those  of  all  the  orbits 
vn.  To  form  a  correct 
igine  them  tipped  orer 
ecliptic,  instead  of  90° 


..  .■■ 


TIIK  PLANET  VltANUft. 


960 


above  it.  The  pole  of  the  orbit  which  ghoiild  be  considered  as  the 
nortli  one  I''  tliat  from  whlcli,  if  nn  observer  loolc  down  upon  n  re- 
volving body,  llie  latter  would  seem  to  turn  in  a  direction  oppoBil* 
tliat  of  the  hundw  of  a  watch.  Wlicn  the  orbit  is  lipi>cd  over  more 
than  a  riglil  nngle,  the  motion  from  a  point  in  the  direction  of  tlie 
north  pole  of  the  ecliptic  will  seem  to  be  the  reverse  of  tids;  It  is 
therefore  sometimes  considered  to  be  retrograde.  This  term  is  fre- 
quently ivpplieti  to  the  motion  of  tlio  satellites  of  Uranut,  but  is 
ratiier  misleading,  since  tlie  motion,  being  nearly  perpendicular  to 
the  ecliptic,  is  not  exactly  expressed  by  the  term. 

The  four  saU-llitcs  move  in  tlie  same  plane.  This  fact  renders  It 
highly  prolmble  tli  llie  planet  Urannt  revolves  on  its  axis  in  the 
same  plnno  with  the  orbits  of  the  satellitea.  and  is  tlierefore  an  oblate 
splieroid  like  the  earth.  This  conclusion  is  founded  on  the  consid* 
erntlon  tliut  if  tlie  planes  of  the  satellites  were  not  Icept  togetlier  by 
gome  cause,  they  would  gradually  deviate  from  each  other  owing  to 
the  attractive  force  of  the  sun  upon  the  planet.  The  different  satel- 
lites would  deviate  by  different  amounU,  and  it  would  Iw  extremely 
improbable  that  all  the  orbits  would  at  any  time  be  found  in  the 
same  plane.  Since  we  see  tiiem  in  the  same  plane,  we  conclude  that 
some  force  keeps  them  there,  and  the  oblateness  of  the  planet  would 
cause  such  a  force. 


^■^ 


CHAPTER  X. 
THE  PLANET  NEPTUNE. 

After  the  planet  Vranua  had  been  observed  for  some 
thirty  years,  tabJos  of  its  motion  were  prepared  by  Bou- 
VABD.  Ho  had  as  data  available  for  this  purpose  not  only 
the  observations  since  1781,  but  also  observations  extend, 
ing  back  as  far  as  1695,  in  which  the  planet  was  observed 
and  supposed  to  be  a  fixed  star.  As  one  of  the  chief  diffi- 
culties in  the  way  of  obtaining  a  theory  of  the  planet's 
motion  was  the  short  period  of  time  during  which  it  had 
been  regularly  observed,  it  was  to  be  supposed  that  these 
ancient  observationa  would  materially  aid  in  obtaining 
exact  accordance  between  the  theory  and  observation.  But 
it  was  found  that,  after  allowing  for  all  perturbations  pro- 
duced by  the  known  planets,  the  ancient  ond  modem 
observations,  though  undoubtedly  referring  to  the  same 
object,  wore  yet  not  to  be  reconciled  with  each  other,  but 
differed  systematically.  Bocvard  was  forced  to  omit  the 
older  observations  in  his  tables,  which  were  published  in 
1830,  and  to  found  his  theory  upon  the  modern  observa- 
tions alone.  By  so  doing,  he  obtained  a  good  agreement 
between  theory  and  the  observations  of  the  few  years 
immediately  succeeding  1820. 

Bocvard  seems  to  have  formulated  the  idea  that  a  pos- 
sible cause  for  the  discrepancies  noted  might  be  the  exist- 
ence of  an  unknown  planet,  but  the  meagre  data  at  his 
disposal  forged  him  to  leave  the  subject  nDtonched,    In 


':^.>H$iii 


Wmmmmu.^^^ 


observed  for  some 
1  prepared  by  Bou- 
is  purpose  not  only 
bservations  extend- 
ilanet  was  observed 
9  of  the  chief  diflS- 
Jry  of  the  planet's 
iring  which  it  had 
apposed  that  these 

aid  in  obtaining 
1  observation.  But 
pertnrbtttions  pro- 
oicnt  and  modem 
rring  to  the  same 
itii  encli  other,  but 
forced  to  omit  the 
were  published  in 
le  modern  observa- 
a  good  agreement 
of  the  few  years 

lie  idea  that  a  pos- 
night  be  the  ezist- 
leagre  data  at  his 
Dt  UDtonched,    In 


THK  PLANET  NBPTUNB. 


307 


1830  it  was  found  that  the  tables  which  represented  the 
motion  of  the  planet  well  in  1820-25  were  20'  in  error,  in 
1840  the  error  was  90',  and  in  1846  it  was  over  120'. 

These  progressive  and  systematic  changes  attracted  the 
attention  of  astronomers  to  the  subject  of  the  theory  of 
the  motion  of  Uranu$.    The  actual  discrepancy  (120')  in 
1845  was  not  a  quantity  large  in  itself.    Two  stars  of  the 
magnitude  of  Uranus,  and  separated  by  only  120',  would 
be  seen  as  one  to  the  unaided  eye.    It  was  on  account  of 
its  systematic  and  progressive  increase  that  suspicion  was 
excited.     Several  astronomers  attacked  the  problem  in 
various  ways.    The  elder  Stbutk,  at  Pulkova,  prosecuted 
a  search  for  a  new  planet  along  with  his  double-star  obser- 
vations; Bbssbl,  at  Koeiiigsberg,  set  a  student  of  his  own, 
Flsmino,  at  a  new  comparison  of  observation  with  theojy, 
in  order  to  furnish  data  ^or  a  new  determination;  Abaqo, 
then  Director  of  the  Observatory  at  Paris,  suggested  this 
subject  in  1845  as  an  interesting  field  of  research  to  Ls 
Vbrbixb,  then  a  rising  mathematician  and  astronomer. 
Mr.  J.  0.  Adams,  a  stndent  in  Cambridge  University, 
England,  had  become  aware  of  the  problems  presented  by 
the  anomalies  in  the  motion  of  Uranu»,  and  had  attacked 
this  question  ai  early  ai  1843.    In  October,  1845,  Adams 
oommnnioated  to  the  Astronomer  Royal  of  England  ele- 
ments of  a  new  planet  so  situated  as  to  produce  the  per- 
turbations of  the  motion  of  Uranus  which  had  actually 
been  observed.    Such  a  prediction  from  an  entirely  un- 
known stndent,  as  Adams  then  was,  did  not  carry  entire 
conviction  with  it.    A  series  of  accidents  prevented  the 
unknown  planet  being  looked  for  by  one  of  the  largest 
teleaoopee   in   England,  and  so  the   matter   apparently 
dropped.    It  may  be  noted,  however,  that  we  now  know 


I 


w 


258 


ASTRONOMY. 


AnAMs'  elemonts  of  the  new  planet  to  have  been  so  near 
the  trnth  that  if  it  had  been  really  looked  for  by  the  power- 
ful telescope  which  afterward  discovered  its  satellite,  it 
could  scarcely  have  failed  oi  detection. 

Bessbl's  pupil  Flemino  died  before  his  work  was  done, 
and  Bessel's  researches  were  temporarily  brought  to  an 
end.  Strut  e's  search  was  unsuccessful.  Only  Lb  Vbr. 
BIER  continued  his  investigations,  and  in  the  most 
thorough  manner.  He  first  computed  anew  the  pertur- 
bation of  Uranus  produced  by  the.  action  of  Jupiter  and 
Saturn.  Then  he  examined  the  nature  of  the  irregulari- 
ties observed.  These  snowed  that  if  th€>  were  caused  by 
an  unknown  planet,  it  coula  uot  bo  between  Saturn  and 
Uranus,  or  else  Saturn  would  have  been  more  afFected 
than  was  the  case. 

The  new  planet  was  outside  of  Uranus  if  it  existed  at 
all,  and  as  a  rough  guide  Bode's  law  was  invoked,  which 
indicated  a  distance  about  twice  that  of  Uranus.  In  the 
summer  ot  1846  Le  Yerbieb  obtained  complete  elements 
of  a  new  planet,  which  would  account  for  the  observed 
irregularities  in  the  motion  of  Uranus,  and  these  were 
published  in  France.  They  were  very  similar  to  those  of 
Adams,  which  had  been  communicated  to  Professor  ChaL' 
LIS,  the  Director  of  the  Observatory  of  Cambridge,  Eng- 
land. 

A  search  was  immediately  begun  by  Challis  for  such 
an  object,  and  as  no  star-maps  were  at  band  for  this  region 
of  the  sky,  he  began  mapping  the  surrounding  stars.  In 
so  doing  the  new  planet  was  actually  observed,  both  on 
August  4th  and  12th,  1846,  but  the  observations  remain- 
ing unreduced,  and  so  the  planetary  nature  of  the  object 
was  not  recognized. 


t  ■.jaitfflfe^','5'-^ 


L 


ave  been  80  near 
for  by  the  power- 
1  its  satellite,  it 

s  work  was  done, 
y  brought  to  an 
Only  Lb  Vbb- 
d  in  the  most 
mew  the  pertur- 
I  of  Jupiter  and 
of  the  irregalari- 
;  were  caused  by 
reen  Saturn  and 
en  more  affected 

i  if  it  existed  at 
i  invoked,  which 
\Uranus.  In  the 
>niplete  elements 
!or  the  observed 

and  these  were 
lilar  to  those  of 
Professor  Qhal- 

ambridge,  Eng- 

HALLis  for  such 
d  for  this  region 
nding  stars.  In 
iserved,  both  on 
rvaiions  remain- 
re  of  the  object 


■'■LI  i.ip 

mm 


THE  PLANET  NEPTUNE. 


In  September  of  the  same  year  Lb  Yebrier  wrote  to 
Dr.  Qallb,  then  Assistant  at  the  Observatory  of  Berlin, 
asking  him  to  search  for  the  new  planet,  and  directing 
him  to  the  place  where  it  should  be  found.  By  the  aid 
of  an  excellent  star-chart  of  this  region,  which  had  just 
been  completed,  the  planet  was  found  September  23d,  1846. 

The  strict  rights  of  discovery  lay  with  Le  Yebrier, 
but  the  common  consent  of  mankind  has  always  credited 


Via.  77. 

Adams  with  an  equal  share  in  the  honor  attached  to  this 
most  brilliant  achievement.  Indeed,  it  was  only  by  the 
most  unfortunate  succession  of  accidents  that  the  discovery 
did  not  attach  to  Adams'  researches.  One  thing  must  in 
fairness  be  said,  and  that  is  that  the  results  of  Lb  Ver- 
BIBB,  which  were  reached  after  a  most  thorough  investi- 
gation of  the  whole  ground,  were  announced  with  an  en- 
tire confidence  which,  perhaps,  was  lacking  in  the  other 
oaso. 


mi 

\  : 


'",t^'p'>Vr'^-'^'"' 


^TTT  .J  r*'?:T:^^^>W"^;%T7S^T^/*  fas.fiL'W^.'S*irwi'''«.«<«wufw«» 


M 


260 


A8TR0N0MT. 


This  brilliant  diacorery  created  more  enthusiasin  than 
eyen  the  discovery  of  Uranus,  as  it  was  by  an  exercise  of 
far  higher  qualities  that  it  was  achieved.  It  appeared  to 
savor  of  the  marvellous  that  a  mathematician  could  say 
to  a  working  astronomer  that  by  pointing  his  telescope  to 
a  certain  small  area,  within  it  should  be  found  a  new 
major  planet.     Yet  so  it  was. 

The  general  nature  of  the  disturbing  force  which  re- 
vealed the  new  planet  may  be  seen  by  Fig.  77,  which 
shows  the  orbits  of  the  two  planets,  and  their  respective 
motions  between  1781  and  1840.  The  inner  orbit  is  that 
of  Uranus,  the  outer  one  that  of  Neptune.  The  arrows 
passing  from  the  former  to  the  latter  show  the  directions 
of  the  attractive  force  of  Neptune.  It  will  be  seen  that 
the  two  planets  were  in  conjunction  in  the  year  1822. 
Since  that  time  Uranus  has,  by  its  more  rapid  motion, 
passed  more  than  90°  beyond  Neptune,  and  will  continue 
to  increase  its  distance  from  the  latter  until  the  begin- 
ning of  the  next  century. 

Our  knowledge  regarding  Neptune  is  mostly  confined  to 
a  few  numbers  representing  the  elements  of  its  motion. 
Its  mean  distance  is  more  than  4,000,000,000  kilometres 
(2,775,000,000  miles);  its  periodic  time  is  164.78  years; 
its  apparent  diameter  is  2.6  seconds,  corresponding  to  a 
true  diameter  of  55,000  kilometres.  Gravity  at  its  surface 
is  about  nine  tenths  of  the  corresponding  terrestrial  surface 
gravity.  Of  its  rotation  and  physical  condition  nothing 
is  known.  Its  color  is  a  pale  greenish  blue.  It  is  attended 
by  one  satellite,  which  was  discovered  by  Mr.  Lassbll,  of 
England,  in  1847.  The  satellite  requires  a  telescope  of 
twelve  inches'  aperture  or  upward  to  be  well  seen. 


Vf-ss^i^r^.a:^ 


I  enthuBiasm  than 
by  an  exercise  of 
d.  It  appeared  to 
aatician  could  say 
ig  his  telescope  to 
be  found  a  new 

a;  force  which  re- 
>y  Fig.  77,  which 
id  their  respective 

inner  orbit  is  that 
'une.  The  arrows 
how  the  directions 

will  be  seen  that 
in  the  year  1822. 
lore  rapid  motion, 

and  will  continue 
r  until  the  begin- 
mostly  confined  to 
nts  of  its  motion. 
000,000  kilometres 
e  is  164.78  years; 
orresponding  to  a 
avity  at  its  surface 
I  terrestrial  surface 
condition  nothing 
Ine.  It  is  attended 
ly  Mr.  Lasssll,  of 
ires  a  telescope  of 
well  seen. 


CHAPTER  XI. 
THE  PHYSICAL  CONSTITUTION  OF  THE  PLANETS. 

It  is  remarkable  that  the  eight  large  planets  of  tlie  solar 
system,  considered  with  respect  to  their  physical  constitu- 
tion as  revealed  by  the  telescope  and  the  spectroscope,  may 
be  divided  into  four  pairs,  the  planets  of  each  pair  liaving 
a  great  similarity,  and  being  quite  different  from  the  ad- 
joining pair. 

Heronry  and  Venos. — Passing  outward  from  the  sun,  the 
first  pair  we  encounter  will  be  Mercury  and  Venus.  The 
most  remarkable  feature  of  these  two  planets  is  a  negative 
rather  than  a  positive  one,  being  thu  entire  absence  of  any 
certain  evidence  of  change  on  their  surfaces.  We  have  al- 
ready shown  that  Venus  has  a  considerable  atmosphere, 
while  there  is  no  evidence  of  any  such  atmosphere  aroiind 
Mercury.  They  hare  therefore  not  boon  proved  alike  in 
this  respect,  yet,  on  tlie  other  hand,  they  have  not  bKsn 
proved  different.  In  every  other  "-espect  than  this  xhe 
sin,  :iarity  appears  perfect.  No  permanent  markings  have 
ever  bet:,  certiriit'v  seen  on  the  disk  of  either.  If,  fA  is 
possible,  the  atmonhcro  of  both  planets  is  filled  with  clouds 
and  vapor  i.o  chnv^e,  no  openings,  and  no  formations 
among  these  clouc^  m.uses  are  visiMe  from  the  earth.  Whnn- 
ever  either  of  tijese  planets  is  in  fi  certain  pcsidon  rulative 
to  the  earth  and  the  sun  H  seemingly  presents  the  same 
appearanut.,  ani  nut  the  slightest  change  occars  in  that 


i 

if 
1:= 


262 


ASTRONOMY. 


appearance  from  the  rotation  of  the  planet  on  its  axis, 
which  every  analogy  of  the  solar  system  leads  us  to  believe 
must  take  place. 

When  studied  with  the  spectroscope,  the  spectra  of  Mer- 
cury and  Venus  do  not  differ  strikingly  from  that  of  the 
sun.  This  would  seem  to  indicate  that  the  atmospheres  of 
these  planets  do.  not  exert  any  decided  absorption  upon  the 
rays  of  light  which  pass  through  them  ;  or,  at  least,  they 
absorb  only  the  same  rays  which  are  absorbed  by  the  at- 
mosphere of  the  sun  and  by  that  of  the  earth.  The  one 
point  of  difference  is  that  the  lines  of  the  spectrum  pro- 
duced by  the  absoipUon  of  our  own  atmosphere  ap^iear 
darker  in  the  spectrum  of  Venus.  If  this  were  so,  it 
would  indicate  that  the  atmosphere  of  Venus  is  similar  in 
constitution  to  that  of  our  earth,  l)ccauso  it  absorbs  the 
same  rays.  But  the  means  of  measuring  the  darkness  of 
the  lines  are  as  yet  so  imperfect  that  it  is  impossible  to 
speak  with  certainty  on  a  point  like  this. 

The  Earth  and  Mars. — These  planets  arc  distinguished 
from  all  the  others  in  that  their  visible  surfaces  are  mark- 
ed by  permanent  features,  which  show  them  to  be  solid, 
and  which  can  be  seen  from  the  otlicr  heavenly  bodies.  It 
is  true  that  we  cannot  study  the  earth  from  any  other 
body,  but  we  can  form  a  very  correct  idea  how  it  would 
look  if  seen  in  this  way  (from  the  moon,  for  instance). 
Wherever  the  atmosphere  was  clear,  the  outlines  of  the 
continents  and  oceans  would  be  visible,  while  they  would 
be  invisible  where  the  air  was  cloudy. 

Now,  so  far  as  we  can  judge  from  observation,  'uade  at 
so  groat  a  distance,  never  much  less  than  forty  millions  of 
miles,  the  planet  Mars  presents  to  our  telescopes  very 
much  the  same  general  appearance  that  the  earth  would  if 


L 


)IaDet  on  its  axis, 
leads  us  to  believe 

he  spectra  of  Mer- 
from  that  of  the 
bhe  atmospheres  of 
)sorptiou  upou  the 
;  or,  at  least,  they 
t)sorbed  by  the  at- 
Q  earth.  The  one 
the  spectrum  pru- 
.tniosphere  ap^iear 
this  were  so,  it 
''enus  is  similar  in 
use  it  absorbs  the 
g  the  dui'kness  of 
it  is  impossible  to 

arc  distinguished 
mrfaces  are  mark- 
them  to  be  solid, 
avenly  bodies.  It 
li  from  any  other 
dea  how  it  would 
on,  for  instance), 
le  outlines  of  the 

while  they  would 

ervation.  'uade  at 
1  forty  millions  of 
ir  telescopes  very 
;he  eerth  would  if 


PHTSlOAL  CONSrtTtrTtON  OF  TBB  PLANETS.    263 

observed  from  an  equally  great  distance.  The  only  ex- 
ception is  that  ihe  visible  surface  of  Mars  is  seemingly  much 
less  obscured  by  clouds  than  that  of  the  earth  would  be.  In 
other  words,  that  planet  has  a  more  sunny  sky  than  ours. 
It  is,  of  course,  impossible  to  say  what  conditions  we  might 
find  could  we  take  a  much  closer  view  of  Mars :  all  we  can 
assert  is,  that  so  far  as  wo  can  judge  from  this  distance, 
its  surface  is  like  that  of  the  eai  th. 

This  supposed  similarity  is  strengthened  by  the  spectro- 
scopic observations. 

Jupiter  and  Satnrn. — The  next  pair  of  planets  is  Jupi- 
ter and  Saturn.  Their  peculiarity  is  that  no  solid  crust 
or  surface  is  visible  from  without.  Tn  this  respect  they 
differ  from  the  earth  and  Mars,  and  resemble  Mercury 
and  Venus.  But  they  differ  from  the  latter  in  the  very 
important  point  that  constant  changes  can  be  seen  going 
on  at  their  surfaces.  The  preponderance  of  evidence  is 
in  favor  of  the  view  that  these  planets  have  no  solid 
crusts  whatever,  but  consist  of  masses  of  molten  matter, 
surrounded  by  envelopes  of  vapor  constantly  rising  from 
the  interior. 

This  view  is  further  strengthened  by  their  very  small 
specific  gravity,  which  can  be  accounted  for  by  supposing 
that  the  liquid  interior  is  nothing  more  than  a  compara- 
tively small  central  core,  and  that  the  greater  part  of  the 
bulk  of  each  planet  is  composed  of  vapor  of  small  density. 

That  the  visible  surfaces  of  Jupiter  and  Saturn  are  cot- 
ered  by  some  kind  of  an  atmosphere  follows  not  only  from 
the  moLion  of  the  cloud  forms  seen  there,  but  from  the 
spectroscopic  observations. 

XTranna  and  Heptune. — These  planets  have  a  strikingly 
similar  aspect  when  seen  through  a  telescope.    They  differ 


L 


264 


ASTRONOMY. 


from  Jupiter  and  Saturn  in  that  no  changes  or  variations 
of  color  or  aspect  can  be  made  out  upon  tlieir  surfaces; 
and  from  the  earth  and  Mars  in  the  absence  of  any  {lerma- 
nent  features.  Telescopically,  therefore,  we  might  classify 
them  with  Mercury  and  Venus,  but  the  spectroscope  re- 
veals a  constitution  entirely  different  from  that  of  any 
other  planets.  The  most  marked  featin-es  of  their  spectra 
are  very  dark  bands,  evidently  produced  by  the  absorption 
of  dense  atmospheres.  Owing  to  the  extreme  faiutness  of 
the  light  which  reaches  us  from  these  distant  bodies,  the 
regular  lines  of  the  solar  spectrum  are  entirely  invisible  in 
their  spectra,  yet  these  dark  bands  which  are  peculiar  to 
them  have  been  seen  by  several  astronomers. 

This  classification  of  the  eight  planets  into  pairs  is  ren- 
dered yet  more  striking  by  the  fact  that  it  applies  to  what 
we  have  been  able  to  discover  respecting  the  rotations  of 
these  bodies.  The  rotation  of  the  inner  pair,  Mercury 
and  Venus,  has  eluded  detection,  notwithstanding  their 
comparative  proximity  to  us.  The  next  pair,  the  earth 
and  Mars,  have  perfectly  definite  times  of  rotation, 
because  their  outer  surfaces  consist  of  solid  crusts,  every 
part  of  which  must  rotate  in  the  same  time.  The  next 
pair,  Jupiter  and  Saturn,  have  well-establish  ed  times 
of  rotation,  but  these  times  are  not  perfectly  definite, 
because  the  surfaces  of  these  planets  axo  not  solid,  and  dif- 
ferent portions  of  their  mass  may  rotate  in  slightly  different 
times.  Jupiter  and  Saturn  liave  also  in  commou  a  very 
rapid  rate  of  rotation.  Finally,  the  outer  pair,  Uranus 
and  Neptune,  seem  to  be  surrounded  by  atmospheres  of 
such  density  that  no  evidence  of  rotation  can  bo  gathered. 
Thus  it  seems  that  of  the  eight  planets  only  the  central 
four  have  yet  certainly  indicated  a  rotation  on  their  axes. 


vMk 


langes  or  variations 
pon  their  surfaces; 
ienco  of  any  ])erma- 
e,  we  might  classify 
le  spectroscope  ro- 
from  that  of  any 
res  of  their  spectra 
by  the  absorption 
xtreme  fuiutness  of 
distant  bodies,  the 
Bntirely  invisible  in 
ich  are  peculiar  to 
lers. 

«  into  pairs  is  ren- 
b  it  applies  to  what 
ig  the  rotations  of 
ner  pair,  Mercury 
withstanding  their 
xt  pair,  the  earth 
imes    of  rotation, 
solid  crusts,  every 
le  time.     The  next 
[•established  times 
perfectly  definite, 
not  solid,  and  dif- 
n  slightly  difFerent 
in  commou  a  very 
uter  pair,  Uranus 
)y  atmospheres  of 
n  can  bo  gathered, 
s  only  the  central 
Du  on  their  axei. 


J 


CHAPTER  XII. 


METEORS. 


PHEMonirA  AKB  CAvnEs  or  ][iraoB& 

DuBiNO  the  present  century  evidence  has  been  collected 
that  countless  masses  of  matter,  far  too  small  to  be  seen 
with  the  most  powerful  telescopes,  are  moving  through 
the  planetary  spaces.  This  evidence  is  afforded  by  the 
phenomenu  of  "aerolites,"  "meteors,"  and  "shooting- 
stars."  Although  these  several  phenomena  have  been  ob> 
served  and  n>>te<i  from  time  to  time  since  the  earliest  his- 
toric era,  it  is  only  recently  that  a  complete  explanation 
has  been  reached. 

Aerolitei. — Bepor^^s  of  the  falling  of  large  masses  of 
stone  or  iron  to  the  earth  have  been  familiar  to  antiqua- 
rian students  for  many  centuries.  The  problem  where 
such  a  body  could  come  from,  or  how  it  conld  get  into  the 
atmosphere  to  fall  down  again,  formerly  seemed  so  nearly 
incapable  of  solution  that  it  required  some  credulity  to 
admit  the  facts.  When  the  evidence  became  so  strong  as 
to  be  indisputable,  theories  of  their  origin  began  to  bo 
propounded.  One  theory  quite  fashionable  in  the  early 
])art  of  this  century  was  that  they  were  thrown  from 
volcanoes  in  the  moon.  This  theory  has  little  to  sup- 
port it. 

The  proof  hat  aerolites  did  renlly  fall  to  the  ground  first  become 
conclusive  by  the  fall  being  connected  with  oth<;r  more  familiar 
phenomena.     Nearly  every  ops  who  is  at  all  observant  of  the 


ASTRomitr. 


hesTens  is  familiar  with  Midt$,  or  flre-balls^brillinnt  objects  hnving 
the  appearance  of  rockets,  which  are  occasionally  seen  moving  with 
great  Telocity  through  the  upper  regions  of  the  atmosphere. 
Scarcely  a  year  passes  in  which  such  a  body  of  extraordinary  bril- 
liancy is  not  seen.  Generally  these  bodies,  bright  though  they  may 
be,  vanish  without  leaving  any  trace,  or  making  themselves  evident 
to  any  sense  but  that  of  sigiit.  But  on  rare  occasions  their  appearance 
is  followed  at  an  interval  of  several  minutes  by  loud  explosions  like 
the  discharge  of  a  battery  of  artillery.  The  fall  of  these  aerolites  is 
always  accompanied  by  light  and  sound,  though  the  light  may  be 
invisible  in  the  daytime. 

When  chemical  analysis  was  applied  to  aerolites,  they  were  proved 
to  be  of  extramundana  origin,  because  they  contained  chemical 
combinations  not  found  in  terrestrial  substances.  It  is  true  that  they 
contained  no  new  chemical  elements,  but  only  a  combination  of  the 
elements  which  are  found  on  the  earth.  These  combinations  are 
now  so  familiar  to  mineralogists  that  they  can  distinguish  an  aerolite 
from  a  mineral  of  terrestrial  origin  by  a  careful  examination.  One 
of  the  most  frequent  components  of  these  bodies  is  iron. 

Keteers. — Although  the  meteora  we  have  described  are  of  dazzling 
brilliancy,  yet  they  run  by  insensible  gradations  into  phenomena, 
which  any  one  can  see  on  any  clear  night.  The  most  brilliant 
meteors  of  all  are  likely  to  be  seen  by  one  person  only  two  or  three 
times  in  bis  life.  Meteors  having  the  appearance  and  brightness  of 
a  diatant  rocket  may  be  seen  several  times  a  year.  Smaller  ones 
occur  more  frequently;  and  if  a  careful  watch  be  kept,  it  will  be 
found  that  several  of  the  faintest  class  of  all,  familiarly  known  as 
ahootinff-itart,  can  be  seen  on  every  clear  night.  We  can  draw  no 
distinction  between  the  most  brilliant  meteor  illuminating  the  whole 
sky,  and  perhaps  making  a  noise  like  thunder,  and  the  faintest 
■hooting-star,  except  one  of  degree.  There  seems  to  be  every  grada- 
tion between  these  extremes,  so  that  all  should  be  traced  to  some 
common  cause. 

Oaue  of  Meteors. — There  is  now  no  doubt  that  all  these  phenomena 
have  s  common  origin,  and  that  they  are  due  to  the  earth  encounter- 
ing innumerable  small  bodies  in  its  annual  course  around  the  sun. 
The  great  difficulty  in  connecting  meteora  with  these  invisible  bodies 
•riseii  from  the  brilliancy  and  rapid  disappearance  of  the  meteors. 
The  question  may  be  asked.  Why  do  they  bum  with  so  great  an  evolu- 
tion of  light  on  reaching  our  atmosphere?  To  answer  this  quecUon 
we  must  have  recourse  to  the  meclutnical  theory  of  heat.  Heat  is  a 
Tibratory  motion  in  the  particles  of  solid  bodies  and  a  progreasive 
motion  in  those  of  gases.    By  making  tliis  motion  more  rapid  we 


n 


rlllinnt  objecti  hnving 
illy  seen  moving  with 
of  the  atmosphere, 
of  extraordinary  bril- 
fht  though  they  may 
?  themselves  evident 
ions  their  appearance 
'  loud  explosions  like 
I  of  these  aerolites  is 
Sh  the  light  may  be 

;e8,  they  were  proved 

contained  chemical 

■  It  is  true  that  they 

combination  of  the 

se  combinations  are 

stinguish  an  aerolite 

examination.    One 

is  iron. 

'ibed  are  of  dazzling 
IS  into  phenomena. 
The  most  brilliant 
1  only  two  or  three 
'■e  and  brightness  of 
ear.  Smaller  ones 
be  kept,  it  will  be 
»miliarly  known  as 
We  can  draw  no 
ninating  the  whole 
r,  and  the  faintest 

I  to  be  every  grada- 
be  traced  to  some 

II  these  phenomena 
le  earth  encounter- 
■■e  around  the  sun. 
eae  invisible  bodies 
ce  of  the  meteors. 

>  so  great  an  evolu- 
iwer.  this  question 
f  beat.  Heat  is  a 
and  a  progressive 
on  more  npid  we 


METBORS. 


267 


fhake  the  body  warmer.  By  simply  blowing  air  against  any  com- 
bustible body  with  sufficient  velocity  it  can  be  set  on  Are,  and,  if 
incombustible,  the  body  will  be  made  red-hot  and  finally  melted. 
Experiments  to  determine  the  degree  of  temperature  tlius  produced 
have  been  made  which  siiow  tiiat  a  velocity  of  about  50  metres  per 
second  corresponds  to  a  rise  of  temperature  of  one  degree  Centi- 
grade. From  this  the  temperature  due  to  any  velocity  can  be  readily 
cnlnuiated  on  the  principle  that  the  increa&e  of  temperature  is  pro- 
poi'tionul  to  tlie  "energ}'"  of  the  particles,  which  again  is  propor- 
tional to  the  square  of  tlie  velocity.  Hence  a  velocity  of  600  metres 
per  second  would  correspond  to  a  rise  of  100°  above  the  actual  tem- 
perature of  the  air,  so  tiiat  if  the  latter  was  at  the  freezing-point  the 
body  would  be  raised  to  tlie  temperature  of  boiling  water.  A  velocity 
of  1500  metres  per  second  would  produce  a  red  heat 

The  earth  moves  around  the  sun  with  a  velocity  of  about  80,000 
metres  per  second;  consequently  if  it  met  a  body  at  rest  (he  concus- 
sion between  the  latter  and  the  atmosphere  would  correspond  to  a 
temperature  of  more  than  800,000°.  This  would  instantly  dissolve 
any  known  substance. 

It  must  be  remembered  that  when  we  speak  of  these .  enormous 
temperatures,  we  are  to  consider  them  as  potgntial,  not  actual,  tem- 
peratures. We  do  not  mean  that  the  body  is  actually  raised  to  a 
temperature  of  800,000°,  but  only  that  the  air  acts  upon  it  as  if  it 
were  put  into  a  furnace  heated  to  this  temperature;  that  is.  It  is 
rapidly  destroyed  by  the  intensity  of  the  heat. 

This  potential  temperature  is  independent  of  the  density  of  the 
medium,  being  the  same  in  the  rarest  as  in  the  densest  atmosphere. 
But  tiie  actual  effect  on  the  body  is  not  so  great  in  a  rare  as  in  a 
dense  atmosphere.  Every  one  knows  that  he  can  hold  his  hand 
for  some  time  in  air  at  the  temperature  of  boiling  water.  The  rarer 
the  air  the  higher  the  temperature  the  hand  would  bear  without 
injury.  In  an  atmosphere  as  rare  as  ours  at  the  height  of  60  miles, 
it  is  probable  that  the  hand  could  be  held  for  an  indefinite  period, 
though  its  temperature  should  be  that  of  red-bet  Iron;  hence  the 
meteor  is  not  consumed  so  rapidly  as  if  it  struck  a  dense  atmosphere 
with  planetary  velocity.  In  the  latter  case  it  would  probably  dis- 
appear like  a  flash  of  lightning. 

The  amount  of  heat  evolved  is  measured  not  by  that  which 
would  result  from  the  combustion  of  the  body,  but  by  the  «w  viva 
(energy  of  motion)  which  the  body  loses  in  the  atmosphere.  The 
student  of  phystte  knows  that  motion,  when  lost,  is  changed  into  a 
definite  amount  of  heat.  If  we  calculate  the  amount  of  heat  which 
is  equivalent  to  the  energy  of  motion  of  a  pebble  having  a  velocity 


AH 


i 


■m 


r 
1 


368 


ASTBONOMT. 


of  20  miles  a  second,  we  shall  And  it  sufflcient  to  raise  about  1800 
times  tiie  pebble's  weigiit  of  water  from  the  freezing  to  the  Imiling 
point.  This  is  many  times  as  much  heat  as  could  result  from  burn- 
ing eveci  Uit  most  combustible  body. 

The  deti><tation  wh'ch  sometimes  accompanies  the  passage  of 
very  brilliant  meteors  is  not  caused  by  an  Mplosion  of  the  meleor, 
but  by  the  concussion  produced  by  its  rapid  motion  through  our  at- 
mosphere. This  concussion  is  of  much  the  same  nature  as  that  pro- 
duced by  a  flash  of  lightning.  The  air  is  suddenly  condensed  in 
front  of  tlio  meteor,  while  a  vacuum  is  left  behind  it. 

The  invisible  bodies  which  produce  meteors  in  the  way  Just  de- 
scribed have  been  called  meUoroidi.  Meteoric  phenomena  depend 
very  largely  upon  the  nature  of  the  meteoroids,  and  the  direction  and 
velocity  with  which  they  are  moving  relatively  to  the  earth.  With 
very  rare  exceptions,  they  are  so  small  and  fusible  as  to  be  entirely 
dissipated  in  the  upper  regions  of  the  atmosphere.  Even  of  those 
so  hard  and  solicf  ae  to  produce  a  brilliant  light  and  the  loudest  deto* 
nation,  only  a  sn  all  proportion  reach  tlie  earth.  On  rare  occasions 
the  body  is  so  hard  and  massive  as  to  reach  the  canh  without  being 
entirely  consumed.  The  potential  heat  produced  by  its  passage 
through  the  atmosphere  is  then  all  expended  in  melting  and  destroy- 
ing its  outer  layers,  the  inner  nucleus  remaining  unchanged.  When 
sucli  a  body  first  strikes  the  denser  portion  of  the  atmosphere,  the 
resistarce  becomes  so  great  that  the  body  is  generally  broken  to 
pieces.  Hence  we  very  often  And  not  simply  a  single  aerolite,  but  a 
small  shower  of  them. 

Balghts  ef  Meteers.— Many  observations  have  been  made  to  deter^ 
mine  the  height  at  which  meteors  are  seen.  This  is  effected  by  two 
observers  stationing  themselves  several  miles  apart  and  mapping  out 
the  courses  of  such  meteors  as  they  can  observe.  In  the  case  of  very 
brilliant  meteors,  the  path  is  often  determined  with  considerable  pre- 
cision by  tlie  direction  in  which  it  ic  seen  by  accidental  observers  in 
various  regions  of  the  country  over  which  it  passes.  This  observa- 
tion is  nothing  but  a  simultaneous  determination  of  the  parallax  of  a 
meteor  as  seen  from  two  stations.    Bee  Fig.  17. 

Meteors  and  shooting-stara  commonly  commence  to  be  visible  at  a 
height  of  about  100  kilometres,  or  100  statute  miles.  The  separaifl 
resulu  vary  widely,  but  this  is  a  rough  mean  of  them.  They 
are  generally  dissipated  at  about  half  this  height,  and  tberefora 
above  the  highest  atmosphere  which  reflects  the  rays  of  the  sun. 
From  this  It  may  be  inferred  that  the  earth's  atmoaphere  rises  to  a 
height  of  at  least  160  kilometres.  This  is  a  much  greater  hei^t  thaa 
it  ITM  formerly  suppoacd  to  have. 


Dk  to  niM  about  1800 
reexiDg  to  the  Iwiling 
mid  result  from  burn- 

tnlea  the  psasage  of 
plosion  of  the  meteor, 
lotion  through  our  at> 
lue  nature  ns  that  pro- 
iddeoly  condensed  in 
lind  it. 

I  in  the  way  just  de- 
E  phenomena  depend 
and  the  direction  and 
r  to  the  earth.  With 
isible  OS  to  be  entirely 
there.  Even  of  those 
;  and  the  loudest  deto* 
1.  On  rare  occasions 
!  earth  without  being 
luced  by  its  passage 
I  melting  and  destroy- 
g  unchanged.  Whra 
'  the  atmosphere,  the 
I  generally  broken  to 
i  single  aerolite,  but  a 

been  made  to  deter^ 
his  is  effected  by  two 
mrt  and  mapping  out 
I.  In  the  case  of  very 
rith  considerable  pre- 
cidental  obserrers  in 
uses.  This  observo- 
n  of  the  parallax  of  a 

ince  to  be  Tisible  at  a 
miles.  The  separate 
an  of  them.  They 
eight,  and  therefore 
the  rays  of  the  sua. 
tmoaphere  rises  to  a 
h  greater  height  thaa 


MKTBOnS. 


XXTZOBIO  SHOWIM. 

As  already  stated,  the  i»hcnomenft  of  shooting-stars  may 
bo  seen  by  a  careful  observer  on  almost  any  clear  night. 
In  general,  not  more  than  three  or  four  of  them  will  be 
seen  in  an  hour,  and  these  will  be  so  minute  as  hardly  to 
attract  notice.  But  they  sometimes  fall  in  such  numbers 
as  to  present  the  appearance  of  a  meteoric  shower.  On 
rare  occasions  the  shower  has  been  so  striking  as  to  fill  the 
beholi  «  '  with  terror.  The  ancient  and  mediffival  records 
contain  m  v  accounts  of  these  phenomena  which  have  been 
brought  *  t  through  the  researches  of  antiquarians. 

It  has  i  ,.g  been  known  that  some  showers  of  this  class 
occur  at  an  interval  of  about  a  third  of  a  century.  One 
was  observed  by  Humboldt,  on  the  Andes,  on  the  night  of 
November  i2th,  1799,  lasting  from  two  o'clock  until  day- 
light. A  great  shower  was  seen  in  this  country  in  1833, 
and  is  well  known  to  have  struck  the  negroes  of  the 
Southern  States  with  terror.  The  theory  that  the  showers 
occar  at  intervals  of  84  years  was  propounded  by  Glbers, 
who  predicted  a  return  of  the  shower  in  1867.  This  pre- 
diction was  completely  fulfilled,  but  instead  of  appearing 
in  the  year  1867  only,  it  was  first  noticed  in  1866.  On  the 
night  of  November  13th  of  that  year  a  remarkable  shower 
was  seen  in  Enrope,  while  on  the  corresponding  night  of 
the  year  following  it  was  again  seen  in  this  conntiy,  and, 
in  fact,  was  repeated  for  two  or  three  years,  gradually  dy- 
ing away. 

The  oconrrence  of  a  shower  of  meteors  evidently  shows 
that  the  earth  encounters  a  swarm  of  meteoroids.  The  re- 
currence at  the  same  time  of  the  year,  when  the  eart  his 
in  the  same  point  of  its  orbit,  shows  that  the  earth  meets 


1 


270 


ASTRONOMY. 


tho  swarm  at  the  same  point  in  successivo  years.  All  the 
motooroids  of  tho  swurm  must  of  course  bo  moving  in  the 
same  diruction,  elso  they  would  soon  bo  widely  scattered. 
This  motion  is  connected  witli  the  radiant  point,  a  well- 
marked  feature  of  u  meteoric  shower. 

XadUat  Polat. — Suppose  that,  during  a  meteoric  k)i<>  v>ir,  we  iivirk 
the  path  of  each  meteor  on  a  star-map,  nti  in  tlic  flgiii  -  t;°  we  con 
tiniio  the  paths  backward  in  a  straight  line,  we  sliali  lnui  ili.t  thi'> 
all  meet  near  one  and  tlie  same  point  of  tiio  celcstiul  sphere;  '!,  d.  i^, 
they  move  as  if  they  all  rndiated  from  this  point.  The  latfr  is, 
therefore,  called  the  radiant  point.  In  the  figure  the  lines  do  not  all 
pass  accurately  through  tlie  same  point.  Tiiis  la  owing  to  the  un- 
avoidnlilo  errors  made  in  marking  out  the  path. 

It  is  found  that  the  riidiant  point  is  ulviys  in  the  same  position 
among  the  stars,  wherever  tho  observer  iiiti  >'  be  situated,  and  that 
M  tk»  $tan  apparenUy  movt  toward  the  uett,  fhe  radiant  point  mova 
vith  them. 

The  radiant  point  is  due  to  the  fact  that  the  ra<>i<yiroids  which 
atrike  the  earth  during  a  sliower  are  all  moving  in  Oi.  -nme  direc- 
tion. Their  motions  will  all  be  parallel;  hence  whet  he  bodies 
strike  our  atmosphere  the  paths  described  by  them  in  liioir  passage 
will  all  be  parallel  straight  lines.  A  straight  line  seen  by  an  ob- 
server at  any  point  is  pn)jected  as  a  great  circle  of  the  celestial 
■phere,  of  which  the  observer  supposes  himself  to  be  the  centre.  If 
we  draw  a  line  from  tlie  observer  parallel  to  the  patha  of  the  meteors, 
the  direction  of  that  lino  will  represent  a  point  of  the  sphere  through 
which  all  the  paths  will  seem  to  pau;  this  will,  therefore,  be  the 
radiant  point  in  a  meteoric  shower. 

OrUts  of  Mateerie  Ihowas.— From  what  has  Just  been  said  it  will 
be  seen  that  the  position  of  the  radiant  point  indicates  the  direction 
in  which  the  meteoroids  move  relatively  to  the  earth.  If  we  also 
knew  the  velocity  with  which  they  are  really  moving  in  space,  we 
could  make  allowance  for  the  motion  of  the  earth,  and  thus  deter- 
mine the  direction  of  their  actual  motion  in  space.  It  is  not  a  diffi- 
cult problem  to  calculate  the  actual  direction  and  velocity  of  the 
meteoric  swarm  in  space.  Having  this  direction  and  velocity,  the 
orbit  of  the  swarm  around  the  sun  admits  of  Iwing  calculated. 

XeUtioni  of  Keteon  and  Cometa. — The  velocity  of  the 
meteoroids  does  not  admit  of  being  determined  from  obser- 


iivo  years.  All  the 
0  be  moving  in  the 
0  widely  scuttered. 
tiianf  point,  a  well- 


Boric  blxi  vT.  we  iiy\t]f. 
Iio  flgui ;  !.'■  we  con- 
we  shull  U/.!.i  ili^f  tln..^ 
lesliui  sphere;  »!,((,  i<), 
point.  The  latfor  is, 
irc  the  lines  do  not  all 
it  owing  to  the  un- 

n  in  the  same  position 
be  situated,  and  that 
*  radiant  point  m(ne$ 

the  m<^J oiroids  which 
g  in  lis  ^nie  direc- 
ice  wi)i>t  he  bodies 
iiem  in  Mioir  passage 
line  seen  by  an  ob- 
Ircle  of  tlie  celestial 
to  be  the  centra.  If 
patlis  of  the  meteors, 
}f  the  spliere  through 
irill,  therefore,  be  the 

Just  been  said  it  will 
idicates  the  direction 
le  earth.  If  we  also 
moving  in  space,  we 
irtli,  and  thus  deter- 
nce.  It  is  not  a  diffl- 
and  velocity  of  the 
on  and  velocity,  the 
Dg  calculated. 

he  velocity  of  the 
nined  from  obsei'' 


w. 


fVV.;^ 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0   ^''^  ta 


m 
m 


ysiiu  116 


6" 


Fhotographk} 

Sdmces 

Ccffparatian 


23  WKT  MAIN  STIMT 

Wr»rM.N.Y.  I4SM 

(71«)t7S.4S03 


i.wo-KJ'ms^mt^m 


M&&itSM 


»'  i 


CIHM/ICMH 
Collection  de 


I 

\ 


.  ..-WV<V-j,.i.-'.^7.-  'J'.-^VJfittC^I    /.- 


-^^rr. 


METEORS. 


271 


▼ation.     Ono  element  necessary  for  determining  the  orbits 
of  these  bodies  is,  therefore,  wanting.    In  the  case  of  the 


F».  78.— RiBuirr  Ponrr  op  Mimimia  SaowBL 

showers  of  1799,  1833,  and  1866,  commonly  called  the 
November  showers,  this  element  is  given  by  the  time  of 


iiiiimi't.t-t 


272 


ASTRONOMY. 


revolution  around  the  sun.  Since  the  showers  occur  at 
intervals  of  about  a  third  of  a  century,  it  is  highly  proba- 
ble this  is  the  periodic  time  of  the  swarm  around  th  esun. 
The  periodic  time  being  known,  the  velocity  at  any  dis- 
tance from  the  sun  admits  of  calculation  from  the  theory 
of  gravitation.  Thus  we  have  all  the  data  for  determining 
the  real  orbits  of  the  group  of  meteors  around  the  sun. 

Tlie  calculations  necessary  for  this  purpose  were  made 
by  Le  Verrieb  and  other  astronomers  shortly  after  the 
great  shower  of  1866.  The  following  was  the  orbit  as 
given  by  Le  Yerrier: 

Period  of  revolution ." .  88.25  years. 

Ecceutricity  of  orbit 0.9044. 

Least  distance  from  tlie  sun 0.9890. 

Inclination  of  orbit , 165°  19'. 

Longitude  of  the  node 61°  18'. 

Position  of  tlie  perihelion (near  the  node). 

The  publication  of  this  orbit  brought  to  the  attention  of 
the  world  an  extraordinary  coincidence  which  had  never 
before  been  suspected.  In  December,  1865,  a  faint  tele- 
scopic comet  was  discovered.  Its  orbit  was  calculated  as 
follows : 

Period  of  reTolution 88.18  years. 

Eccentricity  of  orbit.   0.9054. 

Least  distance  from  the  sun 0.9765. 

Inclination  of  orbit 168°  43'. 

Longitude  of  the  node 61*  26'. 

LoDgitudo  of  the  perihelion 42°  24'. 

The  publication  of  the  cometary  orbit  and  that  of  the 
orbit  of  the  meteoric  group  were  made  independently  with- 
in a  few  days  of  each  other  by  two  astronomers,  neither  of 
whom  had  any  knowledge  of  the  work  of  the  other.  Oom- 
ijaring  them,  the  result  is  evident.     TIa  swarms  of  meteor- 


'^Bt^Of.' 


METEORS. 


273 


J  showers  occnr  at 
it  is  highly  proba- 
m  around  th  esun. 
elocity  at  any  dis- 
n  from  the  theory 
»ta  for  determining 
round  the  sun. 
lurpose  were  made 
J  shortly  after  the 
was  the  orbit  as 


83.25  years. 
0.9044. 
0.9800. 
166°  19'. 
,    Sr  18'. 
(nenr  the  node). 

to  the  attention  of 
;  which  had  never 
1865,  a  faint  tele- 
was  calculated  as 


88.18  yeara. 
0.9054. 
0.9765. 
163°  43'. 

SI*  26'. 

42°  34'. 

>it  and  that  of  the 
idependently  with- 
nomers,  neither  of 
:  the  other.  Gom- 
swarma  of  meteor' 


Olds  which  cause  the  November  showers  move  in  the  same 
orbit  with  this  comet. 

The  comet  passed  its  perihelion  in  January,  186G.  The 
most  striking  meteoric  shower  commenced  in  the  following 
November,  and  was  repeated  during  several  years.  It 
seems,  therefore,  that  the  meteoroids  which  produce  these 
showers  follow  after  Tempel's  comet,  moving  in  the  same 
orbit  with  it.  This  shows  a  curious  relation  between 
copiets  and  meteors,  of  which  we  shall  speak  more  fully  in 
the  next  chapter.  When  this  fact  was  brought  out,  the 
question  naturally  arose  whether  the  same  thing  might  not 
be  true  of  other  meteoric  showers. 

Other  Showers  of  lleteori.— Although  the  November 
showers  (which  occur  about  November  14)  are  the  only 
ones  so  brilliant  as  to  strike  the  ordinary  eye,  it  has  long 
been  known  that  there  are  other  nights  of  the  year  (nota- 
bly August  10)  in  which  more  shooting-stars  than  usual 
are  seen,  and  in  which  the  large  majority  radiate  from  one 
point  of  the  heavens.  This  shows  conclusively  that  they 
arise  from  swarms  of  meteoroids  moving  together  around 
the  sun. 

The  ZodiMkl  Light.— If  we  observe  the  western  sky  during  the 
winter  or  spring  months,  about  the  end  of  the  evening  twilight,  we 
shall  sec  a  stream  of  faint  light,  a  little  like  the  Milky  Way,  rising 
obliquely  from  the  west,  and  directed  along  the  ecliptic  toward  a 
point  south-west  from  the  zenith.  This  Is  called  the  todiaeal  Ught. 
It  may  also  be  seen  In  the  east  before  daylight  in  the  morning  during 
the  autumn  months,  and  has  sometimes  been  traced  all  the  way 
across  the  heavens.  Ite  origin  is  still  involved  in  obscurity,  but  it 
seems  probable  that  it  arises  from  an  extremely  thin  cloud  either  of 
meteoroids  or  of  semi-gaseous  matter  like  that  composing  the  tail  of 
a  comet,  spread  all  around  the  sun  in  Me  the  earth's  orbit.  lU 
spectrum  Is  probably  that  of  reflpcted  sunlight,  a  result  which  gives 
color  to  the  theory  that  It  wises  from  a  cloud  of  meteoroids  revolv- 
ing round  the  sun. 


^'^^M^ii^ii^.i^h^^-:wJ.^=^^!-rK-lh 


II 


CHAPTER  XIII. 


COMETS. 


Aspect  of  Cohkts. 

Comets  are  distinguished  from  the  planets  both  by  their 
aspects  and  their  motions.  They  ccme  into  view  without 
anything  to  herald  their  approach,  continue  in  sight  for  a 
few  weeks  or  months,  and  then  gradually  vanish  in  the 
distance.  They  are  commonly  considered  as  composed  of 
three  parts:  the  nucleus,  the  coma  (or  hair),  and  the  tail. 

The  nucleus  of  a  comet  is,  to  the  naked  eye,  a  point  of 
light  resembling  a  star  or  planet.  Viewed  in  &  telescope, 
it  generally  has  a  small  disk,  but  shades  off  so  gradually 
that  it  is  difficult  to  estimate  its  magnitude.  In  large 
comets  it  is  sometimes  several  hundred  miles  in  diameter. 

The  nucleus  is  always  surrounded  by  a  mass  of  foggy 
light,  which  is  called  the  coma.  To  the  naked  eye  the 
nucleus  and  coma  together  look  like  a  star  seen  through  a 
mass  of  thin  fog,  which  surrounds  it  with  a  sort  of  halo. 
The  nucleus  and  coma  together  are  generally  called  the 
Jiead  of  the  comet. 

The  iail  of  the  comet  is  simply  a  continuation  of  the 
coma  extending  out  to  a  great  distance,  and  always  di- 
rected away  from  the  sun.  It  has  the  appearance  of  a 
stream  of  milky  light,  which  gi-ows  fainter  and  broader 
as  it  recedes  from  the  head.  Like  the  coma  it  shades  off 
so  gradually  that  it  is  impossible  to  fix  any  boundaries  to 
it.    The  length  of  the  tail  varies  from  3"  or  3°  to  90°  or 


lanets  both  by  their 
)  into  view  without 
inue  in  sight  for  a 
lally  vanish  in  the 
■ed  us  composed  of 
air),  and  the  tail. 
ked  eye,  a  point  of 
ived  in  b  telescope, 
Ics  off  so  gradually 
^nitude.  In  large 
miles  in  diameter, 
y  a  mass  of  foggy 
;he  nuked  eye  the 
tar  seen  through  a 
ith  a  sort  of  halo. 
3uorally  called  the 

}ntinnation  of  the 
!e,  and  always  di- 
3  appearance  of  a 
inter  and  broader 
coma  it  shades  off 
any  boundaries  to 
3"  or  3°  to  90°  op 


I  >  i)»W.i  ''l(Tgi.. 


COMETS. 


275 


more.  Generally  the  more  brilliant  the  head  of  the  comet, 
the  longer  and  brighter  is  the  tail. 

The  above  description  applies  to  comets  which  can  be 
plainly  seen  by  the  naked  eye.  Half  a  dozen  telescopic 
comets  may  be  discovered  in  a  single  year,  while  one  of  the 
brighter  class  may  not  be  seen  for  ten  years  or  more. 

When  comets  are  studied  with  a  telescope,  it  is  found 
that  they  are  subject  to  extraordinary  changes  of  structure. 


Fio.  TV.— Tnnoono  Ooior  without 
A  Nvouro. 


no.  00.— Tbuwomo  Comr  wm 
A  NrcutDS. 


To  understand  these  changes,  we  must  begin  by  saying  that 
comets  do  not,  like  the  planets,  revolve  ai'onnd  the  sun  in 
nearly  circular  orbits,  but  always  in  orbits  so  elongated 
that  the  comet  is  visible  in  only  a  very  small  part  of  its 
course.    See  page  278,  Fig.  82.) 

THB  YAPOBOVS  EHyEIOFE& 

If  a  comet  is  very  small,  it  may  undergo  no  cltanges  of  aspect 
during  its  entire  course.  If  it  is  an  unusually  bright  one,  a  bow 
surrounding  tlie  nucleus  on  the  side  toward  tlie  sun  will  develop 
as  the  comet  approaches  the  sun.  This  bow  will  gradually  rise  up 
and  spread  out  on  all  sides,  finally  assuming  the  form  of  a  semi- 
circle having  the  nucleus  in  its  centre,  or,  to  speak  with  more  pre- 
cision, the  form  of  a  parabola  having  the  nucleus  near  its  focus. 
The  two  ends  of  this  parabola  will  extend  out  further  and  further 
so  M  to  form  a  part  of  tb«  tail,  and  finally  be  lost  in  it.    Other  bows 


Li 


276 


AftTltOXOMT. 


will  successively  form  around  the  nucleus,  nil  slowly  rising  from  It 
like  clouds  of  viipor.  These  distinct  vaporous  mosses  are  culled  the 
entelopea :  they  slimic  oil  grmluidiy  into  the  coma  so  as  to  \>e  witli 
difficulty  distinguished  from  it.  and  indeed  may  Ims  considered  as  part 
of  it.  Tiicsc  appearances  arc  apparently  caused  by  masses  of  vapor 
streaming  up  from  tliat  side  of  the  nucleus  nearest  tiie  sun.  and  grad- 
ually spreading  around  the  comet  on  each  side.  The  form  of  a  bow 
is  not  the  real  form  of  the  envelopes,  but  only  the  apparent  one  in 
which  wo  see  them  projected  against  tlie  bacliground  of  the  sky. 
Perhaps  their  forms  can  be  best  imagined  by  supposing  the  sun  to 
bo  directly  above  the  comet,  and  a  fountain,  throwing  a  liquid  hori- 
zontally  on  all  sides,  to  be  built  upon  that  part  of  the  comet  which 
is  uppermost  Such  a  fountain  would  throw  its  water  in  the  form 
of  ft  sheet,  fftlUng  on  all  sides  of  the  cometic  nucleus,  but  not  touch. 


Wta.  81.— FoMunoM  ov  EimLons. 


ing  it.  Two  or  three  vapor  surfaces  of  this  kind  are  sometimes  seen 
around  the  comet,  the  outer  one  enclosing  each  of  the  inner  ones, 
but  no  two  touching  each  other. 

The  Physical  CoNsniimoH  or  CoMXTa 

To  tell  exactly  what  a  comei.  is.  we  should  be  able  to  show  bow  all 
the  phenomena  it  presents  would  follow  from  the  properties  of  mat- 
ter, as  we  learn  them  at  the  surface  of  the  earth.  This,  however,  no 
one  has  lieen  able  to  do.  many  of  the  phenomena  being  such  as  we 
should  not  expect  from  the  known  constitution  of  matter.  All  we 
can  do,  therefore,  is  to  present  the  principal  characteristics  of  comets, 
as  shown  by  observation,  and  to  explain  what  is  wanting  to  reconcile 
these  characteristics  with  the  known  properties  of  matter. 

In  the  first  place,  all  comets  which  have  been  examined  with  the 
spectroscope  show  a  spectrum  composed,  in  part  at  least,  of  bright 
lines  or  bftnds.    The  positions  and  characters  of  these  bonds  leftYe  M 


COMETS. 


917 


slowly  rising  from  It 
moRses  are  culled  tlie 
■onin  80  as  to  \te  witli 
r  Im3  considered  ns  part 
d  liy  masses  of  vapor 
rest  tiic  sun,  and  grad- 
Tlie  form  of  a  bow 
'  the  apparent  one  in 
cicground  of  the  sliy. 
supposing  the  sun  to 
browing  a  liquid  hori- 
't  of  the  comet  which 
its  water  in  the  form 
ucleiu,  but  not  touch- 


id  are  sometimes  seen 
ih  of  the  inner  ones, 

F  COMXTa 

!  able  to  show  bow  all 
be  properties  of  mat- 
I.  This,  however,  no 
!na  being  such  as  we 
1  of  matter.  All  we 
racteristics  of  comets, 
)  wanting  to  reconcile 
of  matter. 

n  examined  with  the 
rt  at  least,  of  bright 
'  these  bands  lekYe  ao 


doubt  that  carbon,  hydrogen,  and  nitrogen,  and  probably  eaeygen  ar« 
present  in  the  cometary  matter.  More  than  twenty  comets  have  been 
exiimined  since  the  invention  of  the  spectroscope  and  all  agree  in 
giving  the  same  evidence.  In  some  recent  comets  toditim  has  also 
been  discovered. 

In  the  last  chapter  it  was  shown  that  swarms  of  minute  particles 
called  meteoroids  follow  certain  comets  in  their  orbits.  This  is  no 
doubt  true  of  all  comets.  We  can  only  regard  these  meteoroids  as 
fragments  or  debrit  of  the  comet.  On  this  tlieory  a  telescopic  comet 
which  has  no  nucleus  is  simply  a  cloud  of  these  minute  bodies.  The 
nucleus  of  the  brighter  comets  may  either  be  a  more  condensed  mass 
of  such  bodies  or  it  may  be  a  solid  or  liquid  body  itself. 

If  the  reader  has  any  difHculty  in  reconciling  this  theory  of  de- 
tached particles  with  the  view  already  presented,  that  the  envelopes 
from  which  the  tail  of  the  comet  is  formed  consist  of  layers  of  vapor, 
he  must  remember  that  vaporous  masses,  such  as  clouds,  fog,  and 
smoke,  are  really  composed  of  minute  separate  particles  of  water  or 
carbon. 

Vormation  of  ths  Comet's  Tail. — The  tall  of  the  comet  is  not  a  per- 
manent appendage,  but  is  composed  of  the  masses  of  vapor  which 
we  have  already  described  as  ascending  from  the  nucleus,  and  after- 
ward moving  away  from  the  suu.  The  tail  which  we  see  on  one 
evening  is  not  absolutely  the  same  we  saw  the  evening  before,  a  por- 
tion of  the  latter  having  been  dissipated,  while  new  matter  has  taken 
its  place,  as  with  the  stream  of  smoke  from  a  steamship.  The 
motion  of  the  vaporous  matter  which  forms  the  tail  being  always 
away  from  the  sun,  there  seems  to  be  a  repulsive  force  exerted  by 
the  sun  upon  it.  The  form  of  the  comet's  tail,  on  the  supposition 
that  it  is  composed  of  matter  driven  away  from  the  sun  with  a  uni- 
formly accelerated  velocity,  has  been  several  times  investigated,  and 
found  to  represent  the  observed  form  of  the  tail  so  nearly  as  to 
leave  little  doubt  of  its  correctness.  We  may,  therefore,  regard  it  as 
an  observed  fact  that  the  vapor  which  rises  from  the  nucleus  of  the 
comet  is  repelled  by  the  sun  instead  of  being  attracted  toward  it,  as 
larger  masses  of  matter  are. 

No  adequate  explanation  r.'l  this  repulsive  force  has  ever  been 
given.  , 

Konon  or  CkmiTi. 

Previous  to  the  time  of  Newton,  no  certain  knowledge  respecting 
the  actual  motions  of  comets  in  the  heavens  had  been  acquired,  ex- 
cept tlMt  they  did  not  movb  around  the  sun  in  ellipses  like  the  planets. 


278 


ASTRONOMY. 


When  Newton  investigAted  the  mathematical  results  of  the  theory 
of  gravitation,  he  found  that  a  body  moriiig  under  the  nttraction  of 
the  Bim  might  describe  either  of  tlie  three  conic  lectioiiH,  the  eliipse, 
parabola,  or  hyperbola.  Bodies  moving  in  an  ellipse,  as  the  planets, 
would  complete  their  orbits  at  regular  intervals  of  time,  according 
to  laws  already  laid  down.  But  if  the  body  moved  in  a  parabola  or 
an  hyperbola,  it  would  never  return  to  the  sun  after  once  passing  it, 
but  would  move  off  to  inflnity.  It  was,  therefore,  very  natural  to 
conclude  that  comets  might  be  bodies  which  resemble  the  planets  in 
moving  under  the  sun's  attraction,  but  which,  instead  of  describing 


Fro.  n.— Eujrno  and  Pakabouo  Obbits. 

an  ellipse  in  regular  periods,  like  the  planets,  move  in  parabolic  or 
hyperbolic  orbits,  and  therefore  only  approach  the  sun  a  single  time 
during  their  whole  existence. 

This  theory  is  now  known  to  be  essentially  true  for  most  of  the 
observed  comets.  A  few  are  indeed  found  to  be  revolving  around 
the  sun  in  elliptic  orbits,  which  differ  from  those  of  the  planets  only 
in  being  much  more  eccentric.  But  the  greater  number  which  have 
been  observed  have  receded  from  the  sun  in  orbita  which  we  are  un- 
able to  distinguish  from  parabolas,  though  it  is  possible  they  may  be 
eitremely  elongated  ellipses.    Comets  are  therefore  divided  with  re< 


COMETS. 


279 


esults  of  the  theory 
ler  the  Attraction  of 
iectioii8,  the  ellipse, 
ipse,  as  tlie  planets, 
of  time,  according 
ed  in  a  parabola  or 
fter  once  passing  it, 
ire,  very  natural  to 
inblo  the  planets  in 
stead  of  describing 


ins. 

)Te  in  parabolic  or 
le  sun  a  single  time 

le  for  most  of  the 
I  r«volTing  around 
of  the  planets  only 
umber  which  have 
s  which  we  are  un- 
issible  they  may  be 
re  divided  witli  re« 


spcct  to  their  motions  into  two  classes;  {I)  periodic  eomett,  which  are 
known  to  move  in  i-llipiii;  orbits,  uml  to  return  to  tiiu  sun  at  fixed  in- 
tervals; and  (2)  parabolic  eumeU,  apparently  moving  in  parabolas, 
never  to  return. 

The  first  discovery  of  the  periodicity  of  a  comet  wns  made  by  IIai,- 
hBY  iu  connection  willi  the  ^reat  comet  uf  1602.  Examining  the  records 
of  past  observations,  he  found  tliat  a  comet  moving  in  nearly  the 
same  orbit  with  that  of  1682  had  been  seen  in  1607,  and  still  another 
in  1581.  He  was  therefore  led  to  the  conclusion  that  these  three 
comets  were  really  one  and  the  same  object,  returning  to  the  sun  at 
intervals  of  about  76  or  76  years.  Ho  therefore  predicted  that  it 
would  appear  again  about  the  year  1758.    Tlie  comet  was  flrst  seen 


Fla.  n.— Obkt  of  BUujr's  OoiiaT. 

on  Christmas-day,  1758,  and  passed  its  perihelion  March  12th,  1759, 
only  one  month  before  the  predicted  time.  At  present  it  is  possible 
to  predict  the  places  of  some  of  the  best  known  periodic  comets 
almost  as  accurately  as  the  positions  of  the  planets. 

We  give  a  figure  showing  the  position  of  the  orbit  of  Hallkt's 
comet  relative  to  the  orbits  of  the  four  outer  planets.  It  attained  its 
greatest  distance  from  the  sun,  far  beyond  the  orbit  of  Ntptutu, 
about  the  year  1878,  and  then  ccmmencrd  its  return  Journey.  The 
figure  shows  tlio  position  of  the  comet  iu  1874.  It  was  then  far  be- 
yond the  rci^h  of  the  most  powerful  telescope,  but  its  distance  and 
direction  admit  of  being  calculated  with  so  much  precision  that  a 
telescope  could  be  pointed  at  it  at  any  required  moment. 


iiL« 


380 


AsrnoyoMT. 


BlMABKABLI    COMITI 

It  is  familiarly  known  that  bright  comctd  were  in  former 
years  objects  of  great  terror,  being  supposed  to  presage 
the  fall  of  empires,  tlie  death  of  monarchs,  the  approach 
of  earthquakes,  wars,  pestilence,  and  every  other  calamity 
which  could  afflict  mankind.  In  showing  the  entire 
grouudlessnoss  of  such  fears,  science  has  rendered  one  of 
its  greatest  benefits  to  mankind. 

In  1456  the  comet  known  as  Hallet's,  appearing 
when  the  Turks  wore  making  war  on  Christendom,  caused 


Wn.  84.— Mdal  or  nn  OmuT  Comr  of  IMMl. 

such  terror  that  Pope  Calixtus  ordered  prayers  to  be 
offered  in  the  churches  for  protection  against  it.  This 
is  supposed  to  be  the  origin  of  the  popular  myth  that  the 
Pope  once  issued  a  bull  against  the  comet. 

The  number  of  comets  visible  to  the  naked  eye,  so  far  as 
recorded,  has  generally  ranged  from  twenty  to  forty  in  a 
century.  Only  a  small  portion  of  these,  however,  have 
been  so  bright  as  to  excite  universal  notice. 

Comet  of  1680. — One  of  the  most  remarkable  of  these 
brilliant  comets  is  that  of  1680.  It  inspired  such  terror 
that  a  medal,  of  which  wo  present  a  figure,  was  struck 
upon  the  Continent  of  Europe  to  quiet  apprehension.  A 
freo  translation  of  the  inccription  is :  "  The  star  threatens 


COMETS. 


I 

nets  were  in  former 
ipposed  to  presage 
rchs,  the  approach 
rery  other  calamity 
lowing  the  entire 
IS  rendered  one  of 

llet's,  appearing 
iristendom,  caueed 


or  IMMl. 

jred  prayers  to  be 
against  it.    This 
lar  myth  that  the 
(t. 

aked  eye,  so  far  as 
enty  to  forty  in  a 
se,  however,  have 
ce. 

narkable  of  these 
pi  red  such  terror 
Sgure,  was  struck 
apprehension.  A 
rhe  star  threatens 


evil  things;  trost  only  I  God  will  turn  them  to  good." • 
Whot  makes  this  comet  especially  rcmorkable  in  history 
is  that  Newton  calculated  its  orbit,  and  showed  that  il 
moved  around  the  sun  in  a  conic  section,  in  obedience  to 
the  law  of  gravitation. 

Great  Comet  of  1811.— It  has  a  period  of  over  8000 
years,  and  its  aphelion  distance  is  about  40,000,000,000 

miles. 

Qrtftt  Comet  of  1848.— One  of  the  most  brilliant  comet* 
which  have  apiwarcd  during  the  present  century  was  thai 
of  February,  1843.  It  was  visible  in  full  daylight  close  to 
the  sun.  Considerable  terror  was  caused  in  some  qu•^ 
ters  lest  it  might  presage  the  end  of  the  world,  which  had 
been  predicted  for  that  year  by  Miller.  At  perihelion  it 
pMsod  nearer  the  sun  than  any  other  body  has  ever  been 
known  to  pass,  the  least  distance  being  only  about  one 
fifth  of  the  sun's  semidiometer.  With  a  very  slight 
change  of  iU  original  motion,  it  would  have  actually  fallen 

into  the  sun. 

Oreat  Comot  of  1868.— Another  comet  remarkable  for 
the  length  of  time  it  remained  visible  was  that  of  1868. 
It  i>  frequently  called  after  the  name  of  Donati,  its  first 
discoverer.  No  comet  visiting  our  neighborhood  in  recent 
times  has  afforded  so  favorable  an  oi.portunity  for  study- 
inc  it«  Phyical  constitution.  Its  greatest  brilliancy 
occurred  about  the  beginning  of  October,  when  its  tail  was 
40'  in  length  and  10"  in  breadth  at  its  outer  end.  Its  period 
is  1960  years. 

"7^,p;;7;;,;^;;7ri.ouid  notu*  the  c«re  which  ««"""'"»•  "'j»»V'; 

.<«(AtioD  hu  t«ken  to  m«ke  it  cousolalory.  to  make  it  rliymc.  sod 
S^^irimplid?;  U.C  year  of  the  comet  hy  wri.iug  cerUiB  Romwt 
numeral*  krger  than  llie  otiier  letleri. 


^ii 


1  i 


Ito.  8K,--DoiiAn*a  Ooot  or  im. 


COMETS. 


988 


Great  Comet  of  1882. — It  is  yet  too  soon  to  speuk  of  the 
results  of  the  observutions  on  this  magnificent  object.  Its 
splendor  will  not  soon  be  forgotten  by  those  who  have 
seen  it. 

Eneke'i  Comet  ud  the  Xeristing  Medium.— Of  telescopic  comets, 
that  which  has  been  most  investigated  by  astronomers  is  linown  ns 
Enckk's  comet.  Its  period  is  between  three  and  four  years.  Viewed 
witli  a  telescope,  it  is  not  different  in  any  respect  from  otlier  tele- 
scopic comets,  appearing  simply  as  a  mass  of  foggy  light,  somewhat 
brighter  near  one  side.  Under  the  most  favorable  circumstances,  it 
is  just  visible  to  tlie  naked  eye.  The  circumstance  which  has  lent 
most  interest  to  this  comet  is  that  the  olwcrvations  which  have  been 
made  upon  it  seem  to  indicate  that  it  is  gradually  approaching  tho 
sun.  Encke  attributed  this  change  in  its  orbit  to  the  existence  in 
space  of  a  resisting  medium,  so  rare  as  to  have  no  appreciable  effect 
upon  the  motion  of  the  pliuiets,  and  to  be  felt  only  by  bodies  of  ex- 
treme tenuity,  like  the  telescopic  comets.  The  approach  of  the 
comet  to  the  sun  is  shown,  not  by  direct  observation,  but  only  by  a 
gradual  diminution  of  the  period  of  revolution.  It  will  be  many 
centuries  before  thii  period  would  be  so  far  diminished  that  the 
comet  would  actually  touch  the  sun. 

If  the  change  in  the  period  of  this  comet  were  actually  due  to  the 
cause  which  Ekcke  supposed,  then  other  faint  comets  of  the  same 
kind  ought  to  be  subject  to  a  similar  Influence.  But  the  Investiga- 
tions which  have  been  made  in  recent  times  on  these  bodies  show  no 
deviation  of  the  kind.  It  might,  then'fore,  be  concluded  that  the 
change  in  the  period  of  Enckb'b  comet  must  be  due  to  some  other 
cause.  There  is,  however,  one  circumstance  which  leav^  us  in 
doubt.  Enckb's  comet  passes  nearer  the  sun  than  any  other  comet 
of  short  period  which  has  been  observed  with  suiflcient  care  to  de- 
cide the  question.  It  may,  tlierefore,  be  supposed  that  the  resisting 
medium,  whatever  it  may  be,  Is  densest  near  the  sun,  and  does  not 
extend  out  far  enough  for  the  other  comets  to  meet  it.  The  question 
is  one  very  dIfDcult  to  settle.  The  fact  is  that  all  comets  exhibit 
Blight  anomalies  in  their  motions  which  prevent  us  from  deducing 
oouclusions  from  them  with  tho  same  ceruinty  that  we  should  from 
those  of  the  planeU.  One  of  the  chief  difHculties  in  Investigating 
the  orbits  of  comets  with  all  rigor  is  due  to  the  difficulty  of  obtaining 
accurate  positions  of  the  centre  of  so  ill-deflned  an  object  as  the 
nudeos. 


u 


i!rt" 


PART   III. 

THE  UNIVERSE  AT  LARGE. 


II 


INTRODUCTION. 

In  our  studies  of  the  heavenly  bodies,  we  have  hitherto 
been  occupied  almost  entirely  with  those  of  the  solar  sys- 
tem.  Although  this  system  comprises  the  bodies  which 
are  most  important  to  us,  yet  they  form  only  an  insignifi- 
cant part  of  creation.  Besides  the  earth  on  which  we 
dwell,  only  seven  of  the-  bodies  of  the  solar  system  are 
plainly  visible  to  the  naked  eye,  whereas  some  2000  stars 
or  more  can  be  seen  on  any  clear  night. 

The  material  universe,  as  revealed  by  the  telescope,  con- 
sists  principally  of  shining  bodies,  many  miUions  in  num- 
ber a  few  of  the  nearest  and  brightest  of  which  are  visible 
to  the  naked  eye  as  stars.  They  extend  out  as  far  as  the 
most  powerful  telescope  can  penetrate,  and  no  one  knows 
how  much  farther.  Our  sun  is  simply  one  of  these  stars, 
and  does  not,  so  far  as  we  know,  differ  from  its  fellows  in  any 
essential  characteristic.  From  the  moat  careful  estimates, 
it  is  rather  less  bright  than  the  average  of  the  nearer  stars, 
and  overpowers  them  by  its  brilliancy  only  because  it  is  so 

much  nearer  to  us. 

The  distance  of  the  stars  from  each  other,  and  therefore 
from  the  sun,  is  immensely  greater  than  any  of  the  dis- 
tances which  we  have  hitherto  had  to  consider  in  the  soIm 


i^^m^s^mss^t-'- 


286 


ASmONOMT. 


system.  In  fact,  the  nearest  known  star  is  abont  seven 
thousand  times  as  far  as  the  planet  Neptune.  If  we  sup- 
pose the  orbit  of  this  planet  to  be  represented  by  a  child's 
hoop,  the  nearest  star  would  be  three  or  four  miles  away. 
We  have  no  reason  to  suppose  that  contiguous  stars  are,  on 
the  average,  nearer  than  this,  except  in  special  cases  where 
they  are  collected  together  in  clusters. 

The  total  number  of  the  stars  is  estimated  by  millions,  and 
they  are  probably  separated  by  these  wide  intervals.  It 
follows  that,  in  going  from  the  sun  to  the  nearest  star,  we 
would  be  simply  taking  one  step  in  the  universe.  Tlie 
most  distant  stars  visible  in  great  telescopes  are  probably 
several  thousand  times  more  distant  than  the  nearest  one, 
and  we  do  not  know  what  may  lie  be3'ond. 

The  point  wo  Avish  principally  to  impress  on  the  i-eader 
in  this  connection  is  (hat,  although  the  stars  and  planets  pre- 
sent to  the  naked  eye  so  great  a  similarity  in  appeiirance, 
there  is  the  greatest  possible  diversity  in  their  distances 
and  characters.  The  planets,  though  many  millions  of 
miles  away,  are  comparatively  near  us,  and  form  a  little 
family  by  themselves,  which  is  called  the  solar  system. 
The  fixed  stars  are  at  distances  incomparably  greater — the 
nearest  star  being  thousands  of  times  more  distant  than 
the  farthest  planet.  The  planets  are,  so  far  as  we  can  see, 
worlds  somewhat  like  this  on  which  we  live,  while  the  stars 
are  suns,  generally  larger  and  brighter  than  our  own. 
Each  star  may,  for  aught  we  know,  have  planets  revolving 
around  it,  but  their  distance  is  so  immense  that  the  largest 
planets  will  remain  invisible  with  the  most  powerful  tele- 
scopes man  can  ever  hope  to  construct. 

The  classification  of  the  heavenly  bodies  thus  leads  us  to 
this  curious  conclusion.    Our  sun  is  one  of  the  fomily  of 


)wn  star  is  about  seven 
)t  Neptune.  If  we  sup- 
represented  by  a  child's 
iree  or  four  miles  away, 
contiguous  stars  are,  on 
pt  in  special  cases  where 
ers. 

itimatcd  by  millions,  and 

leso  wide  intervals.    It 

to  the  nearest  star,  we 

in  the  universe.    The 

telescopes  are  probably 

it  than  the  nearest  one, 

)eyond. 

)  impress  on  the  i-eader 
he  stars  and  planets  pre- 
milarity  in  appciirance, 
Tsity  in  their  distances 
>ugh  many  millions  of 
iT  us,  and  form  a  little 
died  the  solar  system, 
comparably  greater— the 
mes  more  distant  than 
re,  so  far  as  we  can  see, 
i  we  live,  while  the  stars 
righter  than  our  own. 
,  have  planets  revolving 
nmense  that  the  largest 
the  most  powerful  tele- 
net. 

r  bodies  thus  leads  us  to 
is  one  of  the  family  of 


THE  UNIVERSE  AT  LARGE. 


387 


stars,  the  other  members  of  which  stud  the  heavens  at 
night,  or,  in  other  words,  the  stars  are  suns  like  that  which 
makes  the  day.  The  planets,  though  they  look  like  stars, 
are  not  such,  but  bodies  more  like  the  earth. 

The  great  universe  of  stars,  including  the  creation  in  its 
largest  extent,  is  called  the  stellar  system,  or  stellar 
universe.  We  have  first  to  consider  how  it  looks  to  the 
naked  eye. 


i#; 


m 


»  -i 


CHAPTER  I. 


C0N8TELLATI0N& 

Oekekal  Aspect  or  the  H£AyBH& 

When  we  view  the  licttvens  with  the  unassisted  eye,  the 
stars  apiiear  to  be  scattered  nearly  at  random  over  the 
surface  of  the  celestial  vault.     The  only  deviation  from  an 
entirely  random  distribution  which  can  be  noticed  is  a  cer- 
tain grouping  of   the  brighter  ones  into   constellations. 
A  few  stars  arc  comparatively  much  brighter  than  the  rest, 
and  there  is  every  gradation  of  brilliancy,  from  that  of 
the  brightest  to  those  which  are  barely  visible.     We  also 
notice  at  a  glance  that  the  fainter  stars  outnumber  the 
bright  ones;  so  that  if  we  divide  the  stars  into  classes  ac- 
cording to  their  brilliancy,  the  fainter  classes  will  contain 
the  most  stars. 

The  total  number  one  can  see  will  depend  very  largely 
upon  the  clearness  of  the  atmosphere  and  the  keenneas  of 
the  eye.  There  are  in  the  whole  celestial  sphere  about 
6000  stars  visible  to  an  ordinarily  good  eye.  Of  these, 
however,  we  can  never  see  more  than  a  fraction  at  any 
one  time,  because  one  half  of  the  sphere  is  always  below  the 
horizon.  If  we  conld  see  a  star  in  the  horizon  as  easily  as 
in  the  zenith,  one  half  of  the  whole  number,  or  3000,  would 
be  visible  on  any  clear  night.  But  stars  near  the  horizon 
are  seen  through  bo  great  a  thickness  of  atmosphere  as 
greatly  to  obscure   their  light;    consequently  only  the 


I 


ra 


HXAyXH& 


ho  unassisted  eye,  the 
at  random  over  the 
>nly  deviation  from  an 
:an  be  noticed  is  a  ccr- 
}8  into  constellations, 
brighter  than  the  rest, 
•illiancy,  from  that  of 
iirely  visible.  Wo  also 
•  stars  outnumber  the 
B  stars  into  classes  ac- 
ter  classes  will  contain 

ill  depend  very  largely 
ro  and  the  keenness  of 
celestial  sphere  about 
r  good  eye.  Of  these, 
than  a  fraction  at  any 
liere  is  always  below  the 
the  horizon  as  easily  as 
number,  or  3000,  would 
,  stars  near  the  horizon 
:ness  of  atmosphere  as 
consequently  only  the 


CONSTELLATIONa. 


289 


brightest  ones  can  there  be  seen.  As  a  result  of  this  ob- 
scuration, it  is  not  likely  tliat  more  than  2000  stars  can 
ever  be  taken  in  at  a  single  view  by  any  ordinary  eye. 
About  2000  other  stars  are  so  near  the  south  pole 
that  they  never  rise  in  our  latitudes.  Hence  out  of  the 
6000  supposetl  to  be  visible,  only  4000  ever  como  within 
the  range  of  our  vision,  unless  we  make  a  journey  toward 
the  equator. 

The  Oalaxy.— Another  feature  of  the  heavens,  which  is 
less  striking  than  the  stars,  but  has  been  noticed  from 
the  earliest  times,  is  the  Galaxy,  or  Milky  Way.  This 
object  consists  of  a  mngnificent  stream  or  belt  of  Avhite 
milky  light  10°  or  15°  in  brcadlh,  extending  obliquely 
around  the  celestial  sphere.  During  the  pjiring  months  it 
nearly  coinciiles  wiili  our  horizon  in  the  early  evening, 
but  it  can  readily  be  seen  at  all  other  times  of  the  year 
spannini?  the  heavens  like  an  arch.  It  is  for  a  portion  of 
its  length  split  longitudiually  into  two  parts,  which  remain 
separate  through  many  degrees,  and  are  finally  united 
again.  The  student  will  obtain  a  better  idea  of  it  by 
actual  examination  than  from  any  description.  He  will 
see  that  its  irregularities  of  form  and  lustre  are  such  that 
in  some  places  it  looks  like  a  mass  of  brilliant  clouds. 

Lnoid  and  Teleicopio  Stan. — When  we  view  the  heavens 
with  a  telescope,  we  find  that  there  are  innnmerable  stars 
too  small  to  be  seen  by  the  naked  eye.  We  may  there- 
fore divide  the  stars,  with  respect  to  brightness,  into  two 
great  classes. 

Lofiid  Stan  are  those  which  are  yisible  without  a  tele- 
scope. 

TelMOopie  Stan  are  those  which  are  not  so  visible. 

When  Galilbo  first  directed  his  telescope  to  the  heav- 


990 


ASTRONOMY. 


ens,  about  the  year  1610,  ho  perceived  that  the  Milky 
Way  was  composed  of  stars  too  faint  to  bo  individually 
seen  by  the  unaided  eye.  We  thus  have  the  interesting 
fact  that  although  telescopic  stars  cannot  be  seen  one  by 
one,  yet  in  the  region  of  the  Milky  Way  they  arc  so  numer- 
ous that  they  shine  in  masses  like  brilliant  clouds.  Huy- 
OHENS  in  1656  resolved  a  large  portion  of  the  Galaxy  into 
stars,  and  concluded  that  it  was  composed  entirely  of  them. 
Kepleh  considered  it  to  be  a  vast  ring  of  stars  surround 
ing  the  solar  system,  and  remarked  that  the  sun  must  be 
situated  near  the  centre  of  the  ring.  This  view  agrees 
yery  well  with  the  one  now  received,  only  that  the  stars 
which  form  the  Milky  Way,  instead  of  lying  around  the 
solar  system,  are  at  a  distance  so  vast  as  to  elude  all  our 
powers  of  calculation. 

Such  aro  in  brief  the  more  salient  phenomena  which 
are  presented  to  an  observer  of  the  starry  heavens.  We 
shall  now  consider  how  these  phenomena  have  been  clas- 
sified by  an  arrangement  of  the  stars  according  to  their 
brilliancy  and  their  situation. 

KAOHinrsu  ov  the  Stabs. 

In  ancient  times  tlie  stars  were  arbitrarily  clnssifled  into  siz 
orders  of  magnitude.  The  fourteen  briglitest  visible  in  our  lati- 
tude were  designated  as  of  the  first  magnitude,  while  tboae  which 
were  barely  visible  to  the  nalced  eye  were  said  to  be  of  the  sixth 
magnitude.  This  classificatioD,  it  will  be  noticed,  is  entirely  arbi- 
trary, since  there  are  no  two  stars  which  are  absolutely  of  the  same 
brightness;  that  is,  if  all  the  stars  were  arranged  in  the  order  of 
their  actual  brilliancy,  we  should  find  a  regular  gradation  from  the 
brightest  to  the  faintest,  no  two  being  precisely  the  same.  There- 
fore the  brightest  star  of  nny  one  magnitude  is  about  of  the  same 
brilliancy  with  the  faintest  one  of  the  next  higher  magnitude.  Be- 
tween the  north  pole  and  85°  south  declination  there  are: 


iTT'--,. 


COmTELLA  TI0N8. 


291 


red  that  the  Milky 
t  to  bo  individually 
hare  the  interesting 
mnot  be  seen  one  by 
»y  they  arc  so  numer- 
lliant  clouds.  Huy- 
u  of  the  Galaxy  into 
)8ed  entirely  of  them, 
ig  of  stars  surround 
hat  the  sun  must  be 
g.  This  view  ugroos 
,  only  that  the  stars 
of  lying  around  the 
st  as  to  elude  all  our 

tt  phenomena  which 
starry  heavens.  We 
nena  have  been  clas- 
rs  according  to  their 


Stabs. 

rarily  cinnifled  into  six 
litest  visible  in  our  Ihti- 
litude,  wliile  those  wliich 
I  said  to  lie  of  the  siztli 
noticeu,  is  entirely  arbi- 
ire  absolutely  of  the  same 
arranged  in  the  order  of 
gular  gradation  from  the 
cisely  the  same.  There- 
ude  is  about  of  the  same 
t  higher  magnitude.  Be- 
tion  there  are: 


14  stars  of  the  flrst  magnitude. 


48    " 

second 

16a  " 

third 

818    " 

fourth 

854    " 

flftli 

8974    " 

sixth 

5855  of  the  first  six  magnitudes. 

Of  these,  however,  nearly  2000  of  the  sixth  magnitude  are  so  faint 
that  tliey  can  bo  seen  only  by  an  eye  of  extraordinary  lieenness.  A 
star  of  the  second  magnitude  is  four  tenths  as  bright  as  one  of  the 
first;  one  of  the  third  is  four  tenths  as  bright  as  one  of  the  second, 
and  so  on. 

THB  GomTKILATIOVS  AITS  HAMU  Of  THB  BTABE 

The  earliest  astronomers  divided  the  stars  into  groups, 
called  constellations,  and  gaye  special  proper  names  both 
to  these  groups  and  to  many  of  the  more  conspicuous 
stars. 

We  have  evidence  that  more  than  8000  years  Imfore  the  commence- 
ment of  the  Ciiristian  chronology  the  star  Siiiu;  the  brightest  in  tlie 
heavens,  was  known  to  the  Egyptians  under  the  name  of  Soithii. 
The  seven  stars  of  the  Oreat  Bear,  so  conspicuous  in  our  northern 
sky,  were  known  under  that  name  to  Homer  and  Hesiod,  as  well  as 
the  group  of  the  P'eiada,  or  Seven  Stars,  and  the  constellation  of 
Orion.  Indeeil,  it  would  seem  that  all  the  earlier  civilized  nations. 
Egyptians,  Chinese,  Greeks,  and  Hindoos,  had  some  arbitrary  divi- 
sion of  the  surface  of  the  heavens  into  irregular  and  often  fantastic 
shapes,  which  were  distinguished  by  names. 

In  early  times  the  names  of  heroes  and  animals  were  given  to  the 
constellations,  and  these  designations  have  come  down  to  the  present 
day.  Each  object  was  supposed  to  Iw  painted  on  the  surface  of  the 
heavens,  and  the  stars  were  designated  l>y  tlieir  position  upon  some 
portion  of  the  object.  The  anci<!nt  and  mt-diseval  astronomers  would 
■peak  of  "  the  bright  star  in  the  left  foot  M  Orion,"  "  the  eye  of  the 
BuU,"  "  the  heart  of  the  Imm"  "  the  bead  of  Per$eu$, "  etc.  These 
figures  are  still  retained  upon  some  star-ohaits,  and  are  useful  where 
it  is  desired  to  compare  the  older  descriptions  of  the  constellations 
with  our  modem  maps.    Otherwise  they  have  ceased  to  serve  any 


•  f 


8912 


ASTRONOMY. 


I 


purpose,  and  nro  not  gcutrully  founil  on  mnps  designed  for  purely 
astronomical  uses.  .    ,        i         . 

The  Ariibluns,  who  u«ed  this  clumsy  way  of  dt-siffnatlng  stars, 
gave  special  names  to  u  largo  numlKir  of  the  brighter  onen.  Bome  of 
these  uumos  are  in  comnjon  use  at  the  present  time,  as  Aldebaran, 
Fomalhitiit,  vie. 

In  1654  Bayer,  of  Germany,  mapped  down  the  constellations 
upon  clmrts.  designating  the  brigiilcr  stara  of  each  constellation  by 
the  letters  of  the  Greek  alplmbct.  Wlicn  this  alplial)et  was  exhaust- 
ed  he  Introduced  the  Ictlere  of  the  Roman  alplialwt.  In  general,  the 
brightest  star  was  designated  by  the  first  letter  of  the  alphabet,  a, 
the  next  by  the  following  letter,  (i,  etc. 

On  this  system,  a  star  is  designated  by  a  certain  Greek  letter,  fol- 
lowetl  by  the  genitive  of  the  Latin  name  of  the  constellalion  to  which 
it  belongs.  For  example,  a  Canit  Mnjom,  or,  in  English,  a  of  the 
Great  Dog.  Is  the  designation  of  airiut.  the  brightest  star  In  the 
heavens.  The  seven  stars  of  the  Great  Bear  are  called  a  Urtm  Ma- 
jorie  P  Urta  Mujoi-u,  etc.  Areturue  Is  a  Bodli*.  The  reader  will 
here  see  a  resemblance  to  our  way  of  designating  ludividuale  by  a 
Christian  name  followed  by  the  family  name.  The  Greek  lettera 
furnish  the  Christian  names  of  the  separate  stars,  while  the  name  of 
the  constellation  Is  tliat  of  the  family.  As  there  are  only  fifty  lettera 
in  the  two  alphabets  used  by  Baykh,  It  will  be  seen  that  only  the 
fifty  brightest  stars  In  each  constellation  could  be  designated  by  thla 

method. 

When  by  the  aid  of  the  telescope  many  more  stars  than  these  were 
laid  down,  some  other  method  of  denoting  them  became  neceswwy. 
Plambteed,  who  observed  before  ^nd  after  1700,  prepared  an  ex- 
tensive catalogue  of  stars.  In  whicli  those  of  each  constellation  were 
designated  by  numbers  In  the  order  of  right  ascension.  These  num. 
liers  were  entirely  independent  of  the  designations  of  BATEBr-that 
is.  he  did  not  omit  the  Bayer  stars  from  his  system  of  uumbera,  but 
numbered  them  as  If  they  had  no  Greek  letter.  Hence  those  atars  to 
which  Bayer  applied  letters  have  two  designations,  the  number  and 
the  letter.  The  fainter  stars  are  designated  either  by  their  R.A.  and 
*,  or  by  thfllt  numbers  In  some  catalogue  of  sUrs. 

VxrMBBBIirG  AITS  CATALOOVnTO  THI  STAXI. 

As  telescopic  power  is  increased,  we  still  find  stars  of  fainter  and 
fainter  light.  But  the  number  cannot  go  on  Increasing  foreTer  in 
the  same  ratio  as  with  the  brighter  magnitudes,  because,  If  it  did, 
tbe  whole  sky  would  be  a  blaze  of  starlight. 


•  ,t1llt*1H1»it|iBff1itf^mi^iw 


pH  designed  for  purely 

f  of  dfsifcnatiug  atars, 
trigliter  ones.  Borne  of 
snt  time,  as  Aldebaran, 

)wn  tite  constellations 
if  cacli  cnnstellatioD  by 
8  niplinltel  wos  exhaust- 
^ImlKt.  In  gcnenil,  the 
ter  of  tbe  alpliabet,  a, 

ertaln  Greek  letter,  fol- 
le  constellation  to  which 
or,  in  En);lit)h,  a  of  the 
e  brightest  star  in  tite 
lire  called  a  Urtm  Ma- 
luolit.  The  reader  will 
uating  individuals  by  a 
me.  Tbe  Qreek  letters 
stars,  while  the  name  of 
liere  are  only  flfiy  letters 
11  be  seen  that  only  the 
Id  be  designated  by  this 

ore  stars  than  these  were 
Ihem  became  necessary, 
r  1700,  prcpored  an  ex- 
'  each  constellation  were 
ascension.  These  num. 
:nationB  of  BatbRt— that 
I  system  of  number*,  but 
er.  Hence  those  stars  to 
'nations,  the  number  and 
either  by  their  B.A.  and 
'stars. 

0  THE  STABI. 

find  stars  of  fainter  and 
on  increasing  forerer  in 
tudes,  because,  if  it  did, 


C0N8TELLATT0N8. 


208 


If  telescopes  with  powers  far  exceeding  our  present  ones  were 
made,  they  would  no  doubt  show  new  stars  of  tlie  20th  and  2lRt 
magnitudes.  But  it  is  highly  probable  that  the  numbtr  of  such  suc- 
cessive orders  of  Htors  would  not  increase  in  tlie  same  ratio  ns  is  ob- 
served in  the  8th,  9lli,  and  10th  magnitudes,  for  example.  The 
enormous  lobor  of  estimating  tlie  nunil>er  of  stars  of  Ruch  classes  will 
long  prevent  tiic  accumulation  of  statistics  on  this  question;  but  tliis 
much  is  certain,  that  in  special  regions  of  the  sliy.  which  have  been 
searchingly  examined  by  rarious  telescopes  of  successively  increas- 
ing apertures,  the  numl>er  of  new  stars  found  is  by  no  means  in  pro- 
portion to  the  increased  instrumenlal  power.  If  this  is  found  to  be 
true  elsewlioro,  the  conelusitin  may  Iw  that,  after  all,  tbe  stellar  sys- 
tem can  be  experimentally  shown  to  be  of  finite  extent,  and  to  con- 
tain only  a  finite  number  of  stars. 

We  have  already  staled  timt  in  the  whole  sky  an  eye  of  ayeragn 
power  will  see  about  6000  stars.  With  a  telescope  this  number  is 
greatly  increased,  and  the  most  powerful  telescopes  of  modern  times 
will  probably  show  more  than  20,000,000  stars.  As  no  tnistworthy 
estimate  bus  ever  been  made,  there  is  great  uncertainty  upon  this 
point,  and  the  actual  number  may  range  anywhere  between 
15,000,000  and  40.000,000.  Of  this  number,  not  one  out  of  twenty 
has  ever  been  catalogued  at  all. 

The  southern  sky  lias  many  more  stars  of  the  first  seven  magni- 
tudes than  the  norlliern,  and  the  zones  immediately  north  and  south 
of  the  equator,  although  greater  in  surface  than  any  others  of  the 
same  width  in  declination,  arc  absolutely  poorer  in  such  stars. 

Tills  will  be  much  better  understood  by  consulting  the  graphical 
representation  on  page  294.  On  this  chart  are  laid  down  all  the  stars 
of  the  British  Association  Catalogue  (a  dot  for  each  star),  and  beside 
these  the  Milky  Way  is  represented.  The  relative  richness  of  tlie 
TarioUs  zones  can  be  at  once  seen. 

The  distribution  and  number  of  the  brighter  stars  (1st  to  7th  magni- 
tude) can  be  well  under8too<I  from  this  chart. 

In  Aboelander'b  Durehmwterung  of  the  stars  of  the  northern 
heavens  there  are  recordeil  as  belonging  to  the  northern  hemisphere: 


87 

128 

810 

1.016 

4,838 

18,598 

57,960 

387,544 


10  stars  between  the  1.0  magnitude  and  the  t.9  magnitude. 


2.0 
8.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.9 


2.9 
8.9 
4.9 
6.9 
6.9 
7.9 
8.9 
9.5 


994 


AfiTnOKOMT. 


!>u.'.-is«tM*UKf« 


VoystKlJ.ATtONS. 


m 


i 


In  M  314, 03«  hilars  rrom  llio  flfHl  to  llic  9.5  magnltudcg  nrc  cnu- 
nu!ruU<l  in  the  uorllicrn  sky,  so  Hint  Ihure  unu  almut  000,000  in  IhB 
whole  In  .ivpns. 

Wc  may  readily  foniputo  tlio  amoiiiit  of  light  received  by  the  earth 
on  a  clear  but  inoonlesg  night  from  tiicse  Amn.  Let  us  utisume  tiiat 
the  liriglitncB§  of  an  average  stnf  of  llio  tlrst  magnitude  Ih  u'HiutO.S 
of  that  of  (r  Lyrai.  A  star  of  the  2d  magnitude  will  shine  with  a 
liglit  expressed  by  0.5  X  0.4  =  0.20,  and  so  on.    (See  p.  891.) 


The  total  brightness  of        10 

in 

122 

»10 

1.016 

4.822 

18,593 

67,9«0 


•t 
•I 
It 
<• 
ft 


«• 
(I 


1st  magnitude  stars  is   5.0 

2d 

8«l 

4th 

6lh 

6lh 

7th 

8th        " 


7.4 

10.1 

9.9 

18.0 

32.1 

87.8 

47.4 

8um  = 

142.7 

It  thus  appears  that  from  the  stars  to  the  8th  magnitude,  inclusive, 
we  receive  148  times  as  much  light  ns  from  a  Lyra,  a  Lyra  has 
been  determined  by  ZOLLNKK.to  be  about  44,000,000,000  times  fainter 
tlian  the  sun,  so  that  the  proportion  of  starlight  to  sunlight  can  be 
computed.  It  also  appears  that  the  stars  of  magnitudes  too  high  to 
allow  tliem  to  \va  individually  visible  to  the  naked  eye  are  yet  so 
numerous  as  to  affect  the  general  brightness  of  the  sky  more  than 
the  so-called  lucid  sUirs  (1st  to  Otli  magnitude).  Tiio  sum  of  the  last 
two  numbers  of  the  table  is  greater  thuu  the  sum  of  all  the  others. 

NoTB.— The  individnal  stars  and  constellations  can  be 
better  learned  by  the  student  from  a  Star  Atlas  than  by  wy 
maps  which  can  be  given  on  a  page  so  small  as  these. 


CfiAtTEft  li. 


VARIABLE  AND  TEMPORARY  STARS. 


?  r 


I  t 


8TAX8  REaTJI.MU.T  VABIABLE. 

All  stars  do  not  shine  with  a  constant  light.  Since  the 
middle  of  the  seventeenth  century,  stars  variable  in  bril- 
liancy have  been  known.  The  period  of  a  variable  star 
means  the  interval  of  time  in  which  it  goes  through  all  its 
changes,  and  returns  to  its  original  brilliancy. 

The  most  noted  variable  stars  are  Mint  Ceti  (o  Ceti)  and 
Algol  (/?  Persei).  Mira  appears  about  twelve  times  in 
eleven  years,  and  remains  at  its  greatest  brightness  (some- 
times as  high  as  the  2d  magnitude,  sometimes  not  above 
the  4th)  for  some  time,  then  gradually  decreases  for  about 
74  days,  until  it  becomes  invisible  to  the  naked  eye,  and  so 
remains  for  about  five  or  si^  months.  From  the  time  of 
its  reappearance  as  a  lucid  star  till  the  time  of  its  maximum 
is  about  43  days.  The  mean  period,  or  the  interval  from 
minimum  to  minimum,  is  about  333  days,  but  this  period 
varies  greatly.  The  brilliancy  of  the  star  at  the  maxima 
also  varies. 

Algol  has  been  known  as  a  variable  star  since  1667. 
This  star  is  commonly  of  the  2d  magnitude;  after  remain- 
ing BO  about  2i  days,  it  falls  to  4°>  in  the  short  time  of 
4^  hours,  and  remains  of  4™  for  20  minutes.    It  then  com- 


„'ii?MWW«»(L'4ii)fc    -^  ^mfi^^aaifim 


i 


IRY  STARS. 


BIABLE. 


taut  light.  Since  the 
stars  variable  in  bril- 
iod  of  a  variable  star 
it  goes  through  all  its 
rilliancy. 

Mint  Cell  (o  Ceti)  and 
bont  twelve  times  in 
test  brightness  (some- 
sometimes  not  above 
lly  decreases  for  about 
the  nakerl  eye,  and  so 
i.  From  the  time  of 
3  time  of  its  maximum 
,  or  the  interval  from 
days,  but  this  period 
e  star  at  the  maxima 

iable  star  since  1667. 
pitnde;  after  remain- 
In  the  short  time  of 
ainutes.    It  then  com- 


■t^tmm9umia!0i»^tts.  ■-. 


VABlABLE  AND  TEMPOltABt  STAtiS.  2^ 

mences  to  increase  in  brilliancy,  and  in  another  3i  hours  it 
is  again  of  the  2d  magnitude,  at  which  point  it  remains  for 
the  rest  of  its  period,  about  2"  12". 

These  two  examples  of  the  class  of  variable  stars  give  a 
rough  idea  of  the  extraordinary  nature  of  the  phenomena 
they  present.  A  closer  examination  of  others  discloses 
minor  variations  of  great  complexity  and  apparently  with- 
out law. 

About  90  variable  stars  are  well  known,  and  as  many 
more  are  suspected  to  vary.  In  nearly  all  cases  the  mean 
period  can  be  fairly  well  determined,  though  anomalies  of 
various  kinds  frequently  appear.    The  principal  anomalies 

are: 

First.  The  period  is  seldom  constant.  For  some  stars 
the  changes  of  the  period  seem  to  follow  a  regular  law;  for 
others  no  law  can  be  fi^jed. 

Second.  The  time  from  a  minimum  to  the  next  maxi- 
mum is  usually  shorter  than  from  this  maximum  to  the 
next  minimum. 

mrd.  Some  stars  (as  /3  Lyra)  have  not  only  one  maxi- 
mum between  two  consecutive  principal  minima,  but  two 
such  maxima.  For  ft  Lyra,  according  to  Arqelandeb, 
3*  a"*  after  the  principal  minimum  comes  the  first  maxi-  • 
mum;  then,  3*  7"  after  this,  a  secondary  minimum  in  which 
the  star  is  by  no  means  so  faint  as  in  the  principal  mini- 
mum, and  finally  8*  3"  afterward  comes  the  principal  maxi- 
mum, the  whole  period  being  12*  21"  47«. 

The  course  of  one  period  is  illustmted  In  the  following  Uble, 
supposing  the  period  to  begin  at  0*  0*.  Opposite  each  phase  to 
given  the  inten^ty  of  light  in  terms  of  r  ^y^  =  !• 


998 


A8TnomM7. 


,  t 


PhMM  of  ^  Lorrs. 


Principal  Minimum o*  Qb 

First  Maximum 8*  2'' 

Second  Minimum ,\    6*  9'' 

Principal  Maximum 9*  12'' 

Principal  Minimum ]2*  22" 


ReUUre 
Intoniity. 


0.40 
0.88 
0.58 
0.89 

a4o 


The  periods  of  94  well-determined  variable  stars  being  tabulated, 
it  appears  that  they  are  as  follows: 


Ptoriod  between 

No.  of  Stan. 

18 

1 

4 

4 

5 

9 
14 
18 

Period  between 

No.  of  Stank 

Id.  and  20 d. 
20             50 
50            100 
100            150 
150            200 
200            250 
250            800 
800            850 

850  d.  and  400  d. 
400             460 
450             500 
500             550 
650             600 
600             650 
650             700 
700             750 

18 
8 
8 
0 
0 
1 

0    , 
1 

:s  =  04 

It  is  natural  that  there  should  be  few  known  variables  of  periods 
of  500  days  and  over,  but  it  is  not  a  little  remarkable  that  the  periods 
of  over  half  of  these  variables  should  fall  between  250  and  450  days. 

The  color  of  over  80  per  cent  of  the  variable  stars  is  red  or  orange. 
Red  stars  (of  which  600  to  700  arc  known)  are  now  receiving  close 
attention,  as  there  is  a  strong  likelihood  of  finding  among  them  many 
new  variables. 

The  spectra  of  variable  stars  show  changes  which  appear  to  be 
connected  with  the  variations  in  their  light. 


TXMFOBAST  OB  VlW  STAXI. 

There  are  a  few  cases  known  of  apparently  new  stare  which  have 
suddenly  appeared,  attained  more  or  less  brightness,  and  slowly  de- 
creased in  magnitude,  either  disappearing  totally,  or  finally  remain- 
ing as  comparatively  faint  objecta. 

The  most  famous  one  was  that  of  1572,  which  attained  abrightness 


ReUUr* 

Intoniity. 

....    0* 

Ofc 

0.40 

....     9* 

2" 

088 

....     6* 

9* 

0.58 

....     9* 

12'' 

089 

....  ]2* 

22- 

040 

le  stars  being  tabulated, 


1  between 

No.  of  Stem 

and  400  d. 

18 

460 

8 

600 

8 

S50 

0 

MO 

0 

860 

1 

700 

0    , 

760 

1 

2  = 

=  04 

wn  variables  of  periods 
arkable  that  the  periods 
Iween  260  and  460  days, 
e  stars  is  red  or  orange, 
ire  now  receiving  close 
ding  among  them  many 

[es  wbich  appear  to  be 


TAXI. 

Y  new  stars  which  have 
ghtness,  and  slowly  dc- 
itally,  or  finally  remain- 

ich  attained  abrightness 


tmmaiti 


VAlttASLB  AifD  mitPoniRT  STAM.  SOd 

greater  than  that  of  Biriut  or  JupUtr  and  approached  to  Venu$,  being 
even  visible  to  the  eye  in  daylight.  Ttcho  Brake  first  observed  this 
star  in  November,  1672,  and  watched  its  gradual  increase  in  light 
until  iu  maximum  in  December.  It  then  began  to  diminish  in  bright- 
ness, and  in  January,  1573,  it  was  fainter  than  ^upUer.  In  February 
it  was  of  the  1st  magnitude,  in  April  of  the  2d,  in  July  of  the  8d,  and 
in  October  of  the  4th.  It  continued  to  diminish  until  March,  1574, 
when  it  became  invisible,  as  the  telescope  was  not  then  in  use.  Its 
color,  at  flret  intense  white,  decreased  through  yellow  and  red. 
Wlien  it  arrived  at  the  6th  magnitude  its  color  again  became  white, 
and  so  remained  till  its  disappearance.  Tycho  measured  iU  distance 
carefully  from  nine  stars  near  it,  and  near  iU  place  there  is  now  a  star 
of  tlie  10th  or  11th  magnitude,  which  is  possibly  the  same  star. 

The  history  of  temporary  stars  is  in  general  similar  to  that  of  the 
star  of  1672,  except  that  none  have  attained  so  great  a  degree  of  bril- 
liancy. More  than  a  score  of  such  objects  are  known  to  have  ap- 
peared, many  of  them  before  the  making  of  accurate  observations, 
and  the  conclusion  is  probable  that  many  have  appeared  without 
recognition.  Among  telescopic  stars  there  U  but  a  small  chance  of 
detecting  a  new  or  temporary  star. 

Several  supposed  cases  of  the  disappearance  of  stars  exist,  but  here 
there  are  so  many  possible  sources  of  error  that  great  caution  is  necea- 
sary  in  admitting  them. 

Two  temporary  stars  have  appeared  since  the  invention  of  the  spec- 
troscope (1850).  and  the  conclusions  drawn  from  a  study  of  their  spec- 
tra  are  most  important  as  throwing  light  upon  the  phenomena  of 
variable  stars  in  general. 

The  general  theory  of  variable  stars  which  has  now  the  most  evi- 
dence in  its  favor  is  this:  These  bodies  are,  from  some  general  cause 
not  fully  understood,  subject  to  eruptions  of  glowing  hydrogen  gas 
from  their  interior,  and  to  the  formation  of  dark  spots  on  their  sur- 
faces.  These  eruptions  and  formations  have  in  most  cases  a  greater 
or  less  tendency  to  a  regular  period.  ,  .  .    «, 

In  the  case  of  our  sun  (which  is  a  variable  star)  the  period  is  11 
years,  but  in  the  case  of  many  of  the  stars  it  is  much  shorter.  Ordi- 
narily, as  in  the  case  of  the  sun  alid  of  a  large  majority  of  tiie  stars, 
the  variations  are  too  slight  to  affect  the  total  quantity  of  light  to  any 
visible  extent.  But  in  the  case  of  the  varial)le  slors  this  spot-producing 
power  and  the  liability  to  eruptions  are  very  much  greater,  and  thus 
we  have  changes  of  light  which  can  be  readily  perceived  by  the  eye. 
Some  additional  strength  is  given  to  this  theory  by  the  fact  just  men- 
tioned, that  so  large  a  proportion  of  the  variable  stars  are  red.  It  is  well 
kao«n  that  glowing  bodies  emit  a  larger  proportion  of  red  rays  and 


3i    tf 


800 


ABTROlfOMT. 


a  smaller  proportion  of  blue  ones  the  cooler  tlicy  become.  It  is  there- 
fore probable  that  the  red  stars  have  the  lenst  heat.  This  being  the 
case,  it  is  more  easy  to  produce  spots  on  tlieir  surface;  and  if  their 
outside  surface  is  so  cool  as  to  become  solid,  the  glowing  hydrogen 
from  the  interior  when  it  did  burst  through  would  do  so  with  more 
power  than  if  the  surrounding  shell  were  liquid  or  gaseous. 

There  is,  however,  at  least  one  star  of  which  the  variations  mny  be 
due  to  an  entirely  different  cause;  namely,  Algol.  The  extreme  regu- 
larity with  wliich  the  light  of  this  object  fades  awny  and  disappears 
Buggest<«  the  possibility  that  a  dark  body  may  be  revolving  around  it, 
and  partially  eclipsing  it  at  every  revolution.  Tlie  law  of  variation 
of  its  light  is  so  different  from  that  of  the  light  of  other  variable  stars 
as  to  suggest  a  different  cause^  Most  others  are  near  their  maximum 
for  only  a  small  part  of  their  period,  while  Al^  is  at  its  maximum 
for  nine  tenths  of  it.  Others  are  subject  to  nearly  continuous  changes, 
while  the  light  of  Algol  remains  constant  during  nine  tenths  of  its 
period. 


»emm0^  tmmvk 


tlicy  become.  It  is  there- 
St  lieat.  Tliis  being  tbe 
lieir  surface;  and  if  Ibcir 
(I,  tlie  glowing  liydrogcn 
I  would  do  so  with  more 
quid  or  gaseous, 
icli  tlie  variations  may  be 
Algol.  Tlie  extreme  regu- 
idcs  awny  and  disappears 
ty  be  revolving  around  it, 
in.  The  law  of  variation 
ght  of  other  variable  stars 
B  are  near  their  maximum 
Algol  is  at  its  maximum 
early  continuous  changes, 
during  nine  tenths  of  its 


t!ltA!»Tt:ft  111. 
MULTIPLE   STARS. 

Chasaotxb  or  DoraiB  amd  Multiflb  Staxi. 

When  we  examine  the  heavens  with  telescopes,  we  find 
many  cases  in  which  two  or  more  stars  are  extremely  close 
together,  so  as  to  form  a  pair,  a  triplet,  or  a  group.  It  is 
evident  that  there  are  two  ways  to  account  for  this  appear- 
ance. 

1.  We  may  suppose  that  the  stars  happen  to  lie  nearly 
in  the  same  straight  line  from  us,  but  have  no  connection 
with  each  other.  It  is  evident  that  in  this  case  a  pair  of 
Btars  might  appear  double,  although  the  one  was  hundreds 
or  thousands  of  times  farther  off  than  the  other.  It  is, 
moiwver,  impossible,  from  mere  inspection,  to  determine 
which  is  the  farther  off. 

2.  We  may  suppose  that  the  stars  are  really  near  together, 
as  they  appear,  and  are  to  be  considered  as  forming  a  con- 
nected pair  or  group. 

A  couple  of  stars  in  the  first  case  is  said  to  be  optically 

double. 
Stars  which  are  really  physicaUy  connected  are  said  to  bo 

phyneally  double. 

If  th«  lucid  stars  are  equally  distributed  over  the  celestial  sphere, 
tbe  chances  are  80  to  1  against  any  two  being  within  three  minutes 
of  e«5h  other,  and  the  chances  are  500.000  to  1  against  the  six  visible 
stars  of  the  PtowMfc*  being  accidentally  associated  as  we  see  thetn. 
When  the  millions  of  telescopic  stanaie  conridered.  there  it  a  gnatw 


dod 


ABTItdrnMY. 


Fia.  W.— Tta  QoiamwiM  Sub 


probability  of  such  accidental  juxtaposition.  But  the  probability  of 
many  such  cases  occurring  is  so  extremely  small  that  astronomers 
regard  all  the  closest  pairs  as  physically  connected.  Of  the  600,000 
stars  of  the  first  ten  magnitudes,  about  10,000,  or  one  out  of  every 
90,  has  a  companion  within  a  distance  of  BO"  of  arc.    This  proportion 

is  many  times  greater  than  could  possi- 
bly be  the  result  of  chance  distribution. 
There  arc  several  cases  of  stars  which 
appear  double  to  the  naked  eye.  e  Lyra 
is  such  a  star  and  is  an  interesting  oli- 
ject,  from  the  fact  that  eacli  of  the  two 
stars  which  compose  it  is  itself  double. 
This  minute  pair  of  points,  capable  of 
being  distinguished  as  doub!e  only  by 
the  most  perfect  eye  (without  the  tele- 
scope), is  really  composed  of  two  pairs 
of  stars  wide  apart,  with  a  group  of 
smaller  stars  between  and  around 
them.  The  flguie  ahowa  the  appearance  in  a  telescope  of  consider- 
able power. 

Bevolatioaa  of  BenUe  Stars— Binary  Vysteau.— It  is  evident  that  if 
double  stars  are  endowed  with  the  property  of  mutual  gravitation, 
they  must  be  revolving  around 
each  otlier,  as  the  earth  and 
planets  revolve  around  the  sun, 
else  they  would  be  drawn  to- 
gether as  a  single  star. 

The  method  of  determining 
the  period  of  revolution  of  a 
binary  star  is  illustrated  by  the 
figure,  which  is  supposed  to  rep- 
resent the  field  of  view  of  an  in> 
verting  telescope  pointed  toward 
tlie  south.  The  arrow  shows  the 
direction  of  the  apparent  diur- 
nal motion,  Tlie  telescope  is 
supposed  to  be  so  pointed  that 
tite  brighter  star  may  >ie  in  the 
centre  of  tlie  field.  The  num- 
bers around  the  surrounding 
circle  then  show  the  angle  of 
position,  supposing  the  smaller  star  to  be  in  the  direcUon  of  the 
number. 


87.— Poanoii-AiMUi 
Stab. 


DooBia 


But  the  probabiHty  of 
'  BDiall  that  aMtroDotners 
nected.  Of  the  600,000 
MX),  or  one  out  of  every 
of  arc.  This  proportion 
greater  than  could  possi* 
It  of  chance  distribution, 
reral  cases  of  stars  which 
,0  the  nailed  eye.  e  Lyra 
nd  is  an  interesting  oli- 
ract  that  eacli  of  the  two 
npose  it  is  itself  double, 
tir  of  points,  capable  of 
shed  as  doub!e  only  by 
ct  eye  (without  the  tele- 
IT  composed  of  two  pairs 
apart,  with  a  group  of 
between  and  around 
I  a  telescope  of  consider- 

«.— It  is  evident  that  if 
'  of  mutual  gravitation, 


mov-Amui  ov  a  Donna 
Stab. 


in  tbe  direction  of  the 


f.^ 


MULTIPLE  STABS. 


303 


Fig.  87  is  an  example  of  a  pair  of  stars  in  which  the  position- 

nncle  Is  about  44°.  .  ,       ,  .i.« 

If  by  measures  of  this  sort  extending  through  a  series  of  years,  the 
.llstance  or  position-angle  of  a  pair  of  stars  is  found  to  change  p«i- 
odicaUy,  it  shows  lliat  one  star  is  revolving  around  tl»e  other.  Such 
a  pair  is  called  a  binary  ttar  or  binary  ,y»Um.  The  only  disliuction 
which  we  can  make  between  binary  systems  ond  ordinary  double 
stars  is  founded  on  the  presence  or  absence  of  this  observed  motion. 
It  is  probable  that  nearly  all  the  very  close  double  stars  are  really 
binary  systcns.  but  that  many  hundreds  of  years  are  required  to  per- 
form a  revolution  in  some  Instances,  so  tliat  the  motion  has  not  yet 

been  detected.  .     ..«    t  .  .^» 

The  discovery  of  binary  systems  is  one  of  great  scientific  interest, 
because  from  them  we  loam  that  the  law  of  gravitation  includes  the 
stars  as  well  as  the  solar  system  in  its  scope,  and  may  thus  be  regarded 
as  truly  universal. 


CHAPTER  IV. 


NEBULA  AND  CLUSTERS. 


<  i; 


DnOOVBBT  OF  Hebvls. 

In  the  star-catalogues  of  Ptolemy,  Hevelius,  and  the 
earlier  writers,  there  was  included  a  class  of  nebulous  or 
cloudy  stars,  which  were  in  reality  star-clusters.  They  ap- 
peared to  the  naked  eye  as  masses  of  soft  diffused  light  of 
greater  or  less  extent.  In  this  respect  they  were  quite 
analogous  to  the  Milky  Way.  In  the  telescope,  the  nebu- 
lous appearance  of  these  spots  vanishes,  and  they  are  seen 
to  consist  of  clusters  of  stars. 

As  the  telescope  was  improved,  great  numbers  of  such 
patches  of  light  were  found,  some  of  which  could  be  re- 
solved into  stars,  while  others  could  not.  The  latter  were 
called  nebula  and  the  former  star-clusters. 

About  1656  HuYQHENS  described  the  great  nebula  of 
Orion,  one  of  the  most  remarkable  and  bnlliuiit  of  these 
objects.  During  the  last  century  Messier,  of  Paris,  made 
a  list  of  103  northern  nebula),  and  Lacaille  noted  a  few 
of  those  of  the  southern  sky.  Sir  William  Herscbel 
with  his  great  telescopes  first  gave  proof  of  the  enormous 
number  of  these  masses.  In  1786  ho  published  a  catalogue 
of  one  thousand  new  nebulae  and  clusters.  This  was  fol- 
lowed in  1789  by  a  catalogue  of  a  second  thousand,  and  in 
1802  by  a  third  catalogue  of  five  hundred  new  objects  of 
this  class.    Sir  JoHi^  Herscsel  added  about  two  thou- 


NEBULJl  AND  CLUSTERS. 


805 


ERS. 


[.S. 


,  Hevelius,  and  the 
;Ia88  of  nebulous  or 
'-clusters.  They  ap- 
Boft  diffused  light  of 
Bct  they  were  quite 
telescope,  the  nebu- 
18,  and  they  are  seen 

at  nnmbers  of  such 
which  could  be  re- 
iot.    The  latter  were 
ters. 

the  great  nebula  of 
id  bnlliuiit  of  these 
siER,  of  Paris,  made 
CAiLLB  noted  a  few 

VlLLIAM   HeRSCBEL 

)of  of  the  enormous 
nblished  a  catalogue 
ters.  This  was  fol- 
nd  thousand,  and  in 
3red  new  objects  of 
ed  about  two  thou- 


Mnd  more  nebul».  The  genend  c.  .logue  of  nebulas  and 
clusters  of  stars  of  the  latter  astrouomor,  published  in 
1864,  contains  6079  nebulae.  Over  two  thirds  of  these 
were  first  discovered  by  the  Hbrschels. 

GLunnoATiox  of  Hibto*  aw  CwrmBa 

In  rtudvlnir  these  objects,  the  first  question  we  meet  Is  this:  Are 
all  thSi  tt.  clustei  of  sfr.  which  look  diffused  only  because 
t^yZ  rSsUnt  that  our  tele««>pe.  cnnot  d««tlnguUh  them  Bepu- 
S 'tor  are  some  of  them  in  reality  what  they  seem  to  bo ;  namely, 

''K  ^Tnl^rol  1784  and  1785.  Sir  W..u.-  H-b-chk. 
tool  Z  Slt^iew.  He  considered  the  Milky  Way  "»«»»«»« ».u\» 
LXeriL  of  .tn«.  and  all  nebuto  naturally  ««ned  to  him  to  L«  but 

Bear  in  a  general  mllklnesa  or  nebulosity.  «    ,   j  jt. 

^n  ItIi:  however.  hU  view,  underwent  a  change.  He  had  dls. 
covered  a  MftuioM  tar  (properly  so  called),  or  a  sUr  which  was  un- 
S^ly  rimtar  to  tb!r«Jfounding  .tars,  and  which  was  encom. 
Dossed  by  a  halo  of  nebulous  light.  j  ..  _ 

HTsays:  "Nebul.  can  be  elected  so  that  an  Insensible  gradation 
•hSfuike  place  from  a  coarse  duster  like  the  Pto«to  do^u  to  a 
milky  nebulosity  like  that  in  OHon,  every  intermediate  step  bein? 
repScnted.  This  tends  to  confirm  the  hypothesis  that  all  are  com- 
Doswi  of  Stan  more  or  less  remote. 

^  comparUon  of  Uie  xmoatremet  of  the  series  »  •«T" «""'  f 
and  a  nebulous  star.  Indicates,  however,  that  tht  mbuMtg  about  th, 
ttariitutof  a  ttarrg  nature. 

"  Considering  a  typical  nebulous  star,  and  supposing  the  nucleus 
and  chevelure  to  be  connected,  we  m.iy.  first,  suppose  the  whole 
to  be  of  stars.  In  which  case  either  the  nucleus  Is  enormously 
larger  than  other  stars  of  Ito  stellar  magnitude,  or  the  envelope  is 
composed  of  sUrs  Indefinitely  small;  or.  second,  we  must  odmit  that 
thTitar  \»  involved  in  a  Mning  fluid  of  a  nature  U>taUy  unknou,n  to 

**'"The  shining  fluid  might  exist  Independently  of  stars.  The 
licht  of  this  fluid  Is  no  kind  of  reflection  from  tlie  star  in  the 
centre  If  this  matter  is  self-luminous.  It  seems  more  fit  to  pro- 
duce a  star  by  Ite  condensation  than  to  depend  on  the  star  for  Its 
ezlstcnc*!. 


^r.aif^g.'-^^4^'''/t--^. 


806 


ASTRONOMY. 


"  Both  diffused  nebulositiea  and  planetary  nebulte  are  better  ac« 
counted  for  by  the  liypothesis  of  a  shining  fluid  than  by  supirasing 
tliem  to  be  distant  stars." 

This  was  the  flrst  exnct  statement  of  the  idea  thnt,  beside  stars 
and  star-clusters,  wo  have  in  tlio  universe  a  totally  distinct  series  of 
objects,  probably  much  more  simple  in  tlieir  constitution.  Observa- 
tions on  the  spectra  of  these  bodies  have  entirely  conflrmed  the  con- 
clusions of  Herbchbl. 

Nebulae  and  clusters  wer«  divided  by  Hbimchbl  into  classes.    He 


WtB.  IB.— flnoAL  VmMOtk. 

applied  the  name  planetetrjf  tiOula  to  certain  circular  or  elliptic 
nebulsB  which  in  his  telescope  presented  disks  like  the  planeto. 
^ral  tubidm  are  those  whose  convolutions  have  a  spiral  shape.  This 
class  is  quite  numerous. 

The  different  kinds  of  nebulss  and  clusters  will  be  better  under, 
stood  from  the  cuU  and  descriptions  which  follow  than  by  formal 
definitions.  It  must  be  remembered  that  there  is  an  almost  infinite 
Tkriety  of  such  shapes. 


ry  nebulce  are  better  ms 
fluid  than  by  supiwBing 

le  idea  that,  beside  Btara 

totally  distinct  scries  of 

r  constitution.    OI)serva- 

llrely  cooflrmed  Uie  con- 

lacHSL  into  classes.    He 


NBBVL^  AND  CLU8TSBB, 

4 


tain  circular  or  elliptic 
dislu  lilie  the  planets, 
ive  a  spiral  shape.    This 

•a  wlil  be  belter  under, 
i  folloir  than  by  formal 
era  ia  an  almost  inflnit« 


na.  n.—Vn  Omma  ob 


308 


AtnnoNOMT. 


Btab-Clvstiu 

The  moBt  noted  of  all  the  cliiHter»  i«  the  I^eiade*.  wlitoli  Imve  al- 
ready been  brh'tly  dt-dcrllK'd  in  fonnccllon  with  the  couglelhition 
Tauni».  Tlie  nverngc  niikcd  eye  on  erwily  diHtinguliih  fix  hIius 
wltlilii  It,  but  under  favoruble  conditions  ten,  eleven,  twelve,  or  more 
stuncnn  be  counted.    WItIt  tlio  tclegcoiM),  over  n  hundred  stara  are 

«een. 

The  cluHtcrs  represented  in  Flg».  90  ond  91  are  good  cxamplvR  of 
tlieir  cluwei.  The  first  is  globular  and  contains  sovernl  tliousand 
sninll  stun.  Tlie  second  is  u  cluster  of  about  200  stars,  of  mngni- 
tudcs  varying  from  the  ninth  to  the  thirteenth  and  fourteenth.  In 
which  the  Itrighter  sUrs  are  scattered. 


Fia.  M.— OiiOBOijui  Ouwraa. 


no.  91  — CoMPaaaaaii  Cixtfnm, 


Clusters  nre  probably  Kibject  to  central  powers  or  forces.  This  waa 
seen  by  Sir  WiLMAM  HBBScmet  in  1789.    He  says: 

"  Not  only  were  round  nebula  and  clusters  formed  by  central 
powers,  but  likewise  every  cluster  of  sUrs  or  nebula  that  shows  a 
prndual  condensation  or  increasing  brightness  toward  a  centre. 
This  theory  of  central  power  is  fnlly  established  on  grounds  of  ob^ 
servation  which  cannot  be  overturned. 

"  Clusters  can  be  found  of  10  diameter  with  a  certain  degree  of 
compression  and  stara  of  a  certain  magnitude,  and  smaller  clustcra 
of  4',  8',  or2'  in  diameter,  with  smaller  stara  and  greater  compreasion. 
und  so  on  through  resolvable  nebulae  by  imperceptible  steps,  to  tb« 


'eiadet,  wlitcli  Imve  al- 
with  the  constellutini) 
diHtiiiguUh  fix  Mlius 
leven,  twelve,  or  more 
or  n  huiidiftl  8Ur8  are 

are  good  example*  of 
tains  Mvernl  tliousand 
It  200  stars,  of  mngni- 
ntb  oud  fourtfcentli,  ia 


91  — CoMpaaauii  CLonm, 

venorforcei.  This  wot 

[ernys: 

ten  formed  by  central 

or  nebula  that  shows  a 

Iness  toward  a  centre. 

shed  on  grounds  of  ob^ 

ivlth  a  certain  degree  of 
de,  nnd  smaller  dustera 
ind  greater  comprewion, 
perceptible  steps,  to  tU« 


HKDUL.IS  AND  CLUSTK118. 


809 


smaller  and  faintest  [and  mo«t  diManll  ncbiilie.  Otiicr  vUxnWn  there 
are  wlilcli  le.»,l  to  tliu  iM-llef  llmt  either  tliey  iirc  more  eomprcHKetl  or 
are'c.)inp<»'«'<l  of  hiru'er  nturs.  8|.liericiil  clusters  are  prolml.ly  not 
more  dilTciviit  in  size  among  tlieiiiselveH  tlian  dlfterenl  IntlivUluttlH  of 
plants  of  iIk!  Himie  Kiwcles.  An  it  lins  iK-cn  Hho«  ii  that  the  splierical 
llguro  of  a  cluster  of  slurs  is  owliij?  to  central  powers,  it  follows  that 
those  cliiHters  wliich,  Mleii*  jMribut,  are  the  most  complete  in  tliis 
figure  miiHt  have  been  the  longest  exposed  to  tlio  action  of  liieso 

"Tlio  maturity  of  a  sidereal  system  may  thus  l)e  judged  from  the 
disposition  of  liie  component  parts. 

"  Though  we  cannot  see  any  Inr.ividuol  aebula  pnsa  tlirough  all 
Its  stages  of  life,  we  can  select  particular  ones  In  eacli  peculiar 
aUge,"  and  thus  obtain  a  single  view  of  llielr  entire  course  of  de- 
Telopment. 

BnOTXA  or  HlBTILJt  AID  CltliTlM,  AMD  FiXlD  STAli. 

In  1884,  five  years  after  the  invention  of  the  spectroscope,  the 
exanjlnation  of  the  spectra  of  thj  iicbulo)  led  lo  the  discovery  that 
while  thespectm  of  stars  were  invariably  continuous  and  crossed  with 
dark  lines  similar  to  tlio*  of  the  solar  spectrum,  those  of  many  ne- 
bula were  diteontinuout,  showing  these  bodies  to  be  composed  of 

The  spectruiR  '*  moat  clusters  is  continuous,  indicating  thot  the 
Individual  slaii  a  lri\y  stellar  in  their  nature.  In  a  few  catea, 
however,  clusters  art  composed  of  a  n\ixture  of  nebulosity  (usually 
near  their  centre)  and  of  stars,  nnd  tlie  spectrum  In  such  cases  ia 
compound  in  its  nature,  so  as  to  indicate  radiation  both  by  gaaeoua 
and  solid  matter. 

SnoTBA  or  Fixed  Stasl 

Stellar  spectra  are  found  to  be,  in  the  main,  similar  to  the  solar 
spectrum;  i.e.,  composed  of  a  continuous  band  of  the  prismatic  col- 
ors, across  wliich  dark  line*  or  bands  were  laid,  the  latter  being  fixed 
in  position.  These  results  show  the  fixed  stars  to  resemble  our  own 
sun  in  general  constitution,  and  to  be  composed  of  an  incandescent 
nucleus  surrounded  by  a  gaseous  and  absorptive  atmosphere  of 
lower  temperature.  Tills  atmosphere  around  many  stars  is  dllTerent 
in  constitution  from  that  of  the  sun.  as  is  shown  by  the  different  poal- 
tlou  and  intensity  of  the  various  black  lines  and  bands  which  are  due 
to  the  abaorptive  action  of  the  atmospheres  o(  tb«  st*T«i 


/ 


tmmn 


m' 


810 


ASTRONOMY. 


It  is  probable  that  the  hotter  a  star  is  the  more  simple  a  Bpectrum 
It  has;  for  the  brightest,  and  therefore  probjibly  the  hottest  stars, 
such  as  SiriiM,  give  spectra  sliowiiig  ouly  very  thiclc  hydrogen  liaes 
and  a  few  very  thin  metallic  lines,  while  the  cooler  stars,  such  as 
our  sun,  are  shown  by  their  spectra  to  contain  a  much  larger  num- 
l)er  of  metallic  elements  than  stars  of  the  type  of  Sirina,  but  no 
non-metallic  elements  (oxygen  possibly  excepted).  The  coolest 
stars  give  baud  siicctra  characteristic  of  compounds  of  metallic 
with  non-tuctallic  elements,  and  of  the  uon  metallic  elements  un- 
combined. 

MOTIOH  OF  8TAB8  DT  THX  LlHE  OF  8IOHT. 

Spectroscopic  observations  of  stars  not  only  give  information  in 
regard  to  their  chemical  and  physical  constitution,  but  have  been 
applied  so  as  to  determine  approximately  the  velocity  in  kilometres 
per  second  with  which  the  stars  are  approaching  to  or  recfding  from 
tlie  earth  along  the  line  joining  earth  and  star.  The  theory  of  such  a 
determinati(m  is  briefly  as  follows: 

In  the  solar  spectrum  we  find  a  group  of  dark  lines,  as  a,  b,  e, 
which  always  maintain  their  relative  position.  Prom  laboratory 
experim'^nts,  we  can  show  that  the  tlirec  bright  lines  of  incandescent 
hydrogen  (for  example)  have  always  the  same  relative  position  as 
the  solar  dark  lines  a,  b,  c.  From  tliis  it  is  inferred  that  the  solar 
dark  lines  are  due  to  the  presence  of  hydrogen  in  its  absorptive 
atmosphere. 

Now,  suppose  that  in  a  stellar  spectrum  we  find  three  dark  lines 
a',  V,  e'.  whose  relative  position  is  exactly  the  same  as  that^f  the 
solar  lines  A.  b,  e.  Not  only  is  their  relative  position  the  same,  but 
the  characters  of  the  lines  themselves,  so  fur  as  the  fainter  spectrum 
of  the  star  will  allow  us  to  determine  them,  are  also  similar;  that  is, 
a'  and  a,  V  and  b,  e'  and  e  arc  alike  as  to  thickness,  blackness,  nebu- 
losity of  edges,  etc.  etc.  From  tliis  it  is  inferred  that  the  ftar  really 
contains  in  its  atmosphere  the  substance  whose  existence  has  been 
shown  in  the  sun. 

If  we  contrive  an  apparatus  by  which  the  stellar  spectrum  is  seen 
in  tlie  lower  half,  say,  of  tlie  eye-piece  of  tlic  spectroscope,  while 
the  spectrum  of  hydrogen  is  seen  just  nlx.vc  it,  we  find  in  some 
cases  this  remarkable  piienomenon.  The  three  dark  stellar  lines, 
a',  V,  ef,  instead  of  l)eing  exactly  coincident  with  the  three  hydrogen 
lines  a,  b,  e,  ore  s<'en  to  be  nil  thrown  to  one  side  or  tlie  other  by  a 
like  amount;  that  is,  the  whole  group  a',  bf,  d,  while  preserving  it» 
Illative  distaifces  the  sanie  as  those  of  the  comparison  ^roup  a,  6,  «, 


i'llHltMliarMWBWIIIilHiifl'i'Ji'll  lil'll  J 


■'15:2'* 


ellnr  spectrum  is  seen 
c  spectroscope,  while 
it,  we  find  in  some 
1*0  dark  stellar  lines, 
lb  the  tliree  hydrogen 
ide  or  the  other  by  a 
,  wliiie  preserving  it» 
parlson  ^up  a,  b,  «, 


^^BULM  AND  CLVSTBltS. 


311 


re  simple  a  spectrum 
)ly  the  hottest  stars, 
tbiclc  hydrogen  liaes 
cooler  stars,  such  as 
»  much  larger  num- 
I>e  of  Sirin$,  but  no 
eptcd).  The  coolest 
ipounds  of  metallic 
netallic  elements  un- 


or  Sight. 

r  give  information  in 
iition,  but  have  been 
velocity  in  kilometres 
i;  to  or  receding  from 
The  theory  of  such  a 

lark  lines,  as  a,  b,  e, 
II.  Prom  laboratory 
lines  of  incandescent 
;  relative  position  as 
iferred  that  the  solar 
;en   in   its  absorptive 

And  three  dark  lines 
same  as  tliat^jof  the 
nsilion  the  same,  but 
I  the  fuinler  spectrum 
also  similar;  that  is, 
less,  blackness,  nebu- 
ed  that  (he  ttar  really 
le  existence  has  been 


ts  shifted  toward  either  the  violet  or  red  end  of  the  spectrum  by  a 
small  yet  measurable  amount.  Repeatetl  experiments  by  different 
instruments  and  observers  show  always  a  shifting  in  llie  same  direc- 
tion and  of  like  amount.  The  figure  shows  the  shifting  of  the  F 
line  in  the  spectrum  of  ««««,  compared  with  one  fixed  Une  of 
hydrogen. 

This  displacement  of  the 
spcctml   lines  is  to  be  ac- 
counted for  by  a  motion  of 
the  star  toward  or  from  the 
earth.    It  is  shown  in  Phy- 
sics  that  if  the  source  of 
the  light  which  gives  the 
spectrum  o',  b',  d  is  mov- 
ing away  from  the  earth, 
this  group  will  be  shifted 
toward  the  red  end  of  the 
spectrum;   if    toward   the 
eartli,  then  the  whole  group 
will  be  shifted  toward  the 
blue  end.    The  amount  of 
this  shifting  is  a  function  of 
the  velocity  of  recession  or 
approach,  and  this  velocity 
in  miles  per  second  can  be  calculated  from  the  measured  displace- 
ment.   This  has  been  done  for  many  stars.    The  results  agree  well, 
when  the  difflcult  nature  of  the  research  is  considered.    Tlie  rates  of 
motion  vary  from  insensible  amounts  to  100  kilometres  per  second ; 
and  In  some  cases  agree  remarkably  with  the  velocities  computed 
from  the  proper  motions  and  probable  parallaxes. 


Fio.  93.— F  Lnn  m  Brwrnnm  or  8nm». 


1 ,1 


CHAPTER  V. 
MOTIONS  AND  DISTANCES  OF  THE  STARS. 

Pbofeb  MoTion. 

We  have  already  stated  that,  to  the  unaided  vision,  the 
fixed  stars  appear  to  preserve  the  same  relative  position  in 
the  heavens  through  many  nentnries,  so  that  if  the  an- 
cient astronomers  could  again  see  them,  they  could  hardly 
detect  the  slightest  change  in  their  arrangement.  But 
accurate  measurements  have  shown  that  there  are  slow 
changes  in  the  positions  of  the  brighter  stars,  consisting  in 
a  motion  forward  in  a  straight  line  and  with  uniform 
velocity.  These  motions  are,  for  the  most  part,  so  slow 
that  it  would  require  thousands  of  years  for  the  change  of 
position  to  be  perceptible  to  the  unaided  eye.  They  are 
called  proper  motions,  since  they  are  peculiar  to  the  star 
itself. 

In  general,  the  proper  motions  even  of  the  brightest 
stars  are  only  a  fraction  of  a  second  in  a  year,  so  that 
thouaands  of  years  would  be  required  for  them  to 
change  their  place  in  any  striking  degree,  and  hundreds 
of  thousands  to  make  a  complete  revolution  around  the 
heavens. 

Pbopbb  MoTioir  or  thk  Sqv. 

It  is  a  priori  evident  that  stars,  in  gonertil,  must  have 
proper  motions,  when  once  we  admit  the  universality  of 


PHE  STARS. 


inuided  vision,  the 
elative  position  in 
>  that  if  the  an- 
they  could  hardly 
rrangement.  But 
lat  there  are  slow 
itars,  consisting  in 
rud  with  uniform 
Dost  part,  80  slow 
for  the  change  of 
cd  eye.  They  are 
tcnliar  to  the  star 

1  of  the  brightest 
in  a  year,  so  that 
sd  for  them  to 
pee,  and  hundreds 
Intion  around  the 


iVH. 

{onenil,  must  have 
he  universality  of 


MOTIONS  AND  DiatANCHS  OF  THE!  STAttS.      315) 

gravitation.  That  any  fixed  star  should  be  entirely  at 
rest  would  require  that  the  attractions  on  uU  sides  of  it 
should  be  exactly  balanced.  Any  change  in  the  position 
of  this  star  would  break  up  this  balance,  and  thus,  in  gen- 
eral, it  follows  that  stars  must  be  in  motion,  since  all  of 
them  cannot  occupy  such  a  critical  position  as  has  to  be 

assumed. 

If  but  one  fixed  star  is  in  motion,  this  affects  all  the 
rest,  and  we  cannot  doubt  but  that  every  star,  our  sun 
included,  is  in  motion  by  amounts  which  vary  from  small 
to  great.    If  the  sun  alone  had  a  motion,  and  the  other 
"stars  were  at  rest,  the  consequence  of  this  would  be  that 
all  the  fixed  stars  would  appear  to  be  retreating  en  masse 
from  that  point  in  the  sky  toward  which  we  were  moving. 
Those  nearest  us  would  move  more  rapidly,  those  more 
distant  less  so.     And  in  the  same  way,  the  stars  from 
which  the  solar  system  was  receding  would  seem  to  be 
approaching  each  other.    If  the  stars,  instead  of  being 
quite  at  rest,  as  just  supposed,  had  motions  proper  to 
themselves,  then  we  should  have  a  double  complexity. 
They  would  still  appear  to  an  observer  in  the  solar  system 
to  have  motions.     One  part  of  these  motions  would  be 
truly  proper  to  the  stars,  and  one  part  would  be  due  to  the 
advance  of  the  sun  itself  in  space. 

Observations  can  show  us  only  the  remltant  of  these 
two  motions.  It  is  for  reasoning  to  separate  this  resultant 
into  its  two  components.  At  first  the  question  is  to  deter- 
mine whether  the  results  of  observation  indicate  any  solar 
motion  at  all.  If  there  is  none,  the  proper  motions  of 
stars  will  be  directed  along  all  possible  lines.  If  the  sun 
does  tnily  move,  then  there  will  be  a  general  agreement  m 
the  resultant  motions  of  the  stars  near  the  ends  of  the  line 


t;'!' 


m 


Asrnoxowf. 


{ \V  ■ 


along  which  it.  moves,  while  those  at  the  sides,  io  to  e^k, 
will  show  comparatively  less  systematic  effect.  It  is  as  if 
one  were  riding  in  the  rear  of  a  railway  train  and  watching 
the  rails  over  which  it  has  just  passed.  As  wo  recede  from 
any  point,  the  rails  at  that  point  seem  to  come  nearer  and 
nearer  together. 

If  we  were  passing  through  a  forest,  we  should  see  the 
trunks  of  the  trees  from  which  we  were  going  apparently 
come  nearer  and  nearer  together,  while  those  on  the  sides 
of  us  would  remain  at  their  constant  distance,  and  those  in 
front  would  grow  further  and  further  apart. 

These  phenomena,  which  occur  in  a  case  where  we  are 
sensible  of  our  own  motion,  serve  to  show  how  we  may 
deduce  a  motion,  otherwise  unknown,  from  the  appear- 
ances which  are  presented  by  the  stars  in  space. 

In  this  way,  acting  npon  suggestions  which  had  been 
thrown  out  previously  to  his  own  time,  Herschel  demon- 
started  that  the  sun,  together  with  all  its  system,  was  mov- 
ing through  space  in  an  nnknown  and  majestic  orbit  of  its 
own.  The  centre  round  which  this  motion  is  directed 
cannot  yet  be  assigned.  We  can  only  determine  the  point 
in  the  heavens  toward  which  our  coarse  is  directed — '*  the 
apex  of  solar  motion." 

A  number  of  astronomers  have  since  investigated  this 
motion  with  a  view  of  determining  the  exact  point  in  the 
heavens  toward  which  the  sun  is  moving.  Their  results 
differ  slightly,  but  the  points  toward  which  the  sun  is 
moving  all  fall  in  the  constellation  Hercules.  The  amount 
of  the  motion  is  such  that  if  the  sun  were  viewed  at  right 
angles  to  the  direction  of  motion  from  an  average  star 
of  the  first  magnitude,  it  would  appear  to  move  about  one 
tkiird  of  a  second  per  year. 


•■■"«a>ij>Tt'- 


he  sides,  Ho  to  e^k, 
ic  effect.  It  is  as  if 
iy  train  and  watching 
.  As  wo  recede  from 
1  to  come  nearer  and 

t,  wo  slionld  see  the 
ere  going  apparently 
e  those  on  the  sides 
listance,  and  those  in 
apart. 

a  case  where  we  are 
)  show  how  we  may 
n,  from  the  appear- 
I  in  space. 

ons  which  had  been 
I,  Herschel  demon- 
its  system,  was  mov- 
majestic  orbit  of  its 
I  motion  is  directed 
determine  the  point 
Be  is  directed — "  the 

ce  investigated  this 
e  exact  point  in  the 
Ting.  Their  resalta 
d  which  the  snn  is 
>-culea.  The  amonnt 
were  viewed  at  right 
om  an  average  star 
X  to  move  about  one 


MOTIONS  AND  MSTANCBB  OF  THE  BTAB8.      316 

DUIAVOIS  OV  THX  FIZXS  8TABI. 

The  ancient  astronomers  supposed  aU  the  fixed  stars  to 
be  situated  at  a  short  distance  outside  of  the  orbit  of  the 
planet  Saturn,  then  the  outermost  known  planet.  The 
idea  wa«  prevalent  that  Nature  would  not  waste  space  by 
leaving  a  great  region  beyond  Saturn  entirely  empty. 

When  Copernicus  announced  the  theory  that  the  sun 
was  at  rest  and  the  earth  in  motion  around  it,  the  problem 
of  the  distance  of  the  stars  acquired  a  new  interest.    It  was 
evident  that  if  the  earth  described  an  annual  orbit,  then 
the  stars  would  apiMjar  in  the  course  of  a  year  to  oscillate 
back  and  forth  in  corresponding  orbits,  unless  they  were 
so  immensely  distant  that  these  oscillations  were  too  small 
to  bo  seen.      The  apparent   oscillation  of  Saturn  pro- 
duced in  this  way  was  described  in  Part  I.    It  amounts  to 
some  6°  on  each  side  of  the  mean  position.    These  oscilla- 
tions were,  in  fact,  those  which  the  ancients  represented 
by  the  motion  of  the  planet  around  a  small  epicycle.    But 
no  such  oscillation  had  ever  been  detected  in  a  fixed  star. 
This  fact  seemed  to  present  an  almost  insuperable  difficulty 
in  the  reception  of  the  Copemican  system.    Very  natural- 
ly, therefore,  as  the  instruments  of  observation  were  from 
time  to  time  improved,  this  apparent  annual  oscillation  of 
the  stars  was  ardently  sought  for. 

The  problem  is  identical  with  that  of  the  annual  parallja 
of  the  fixed  stars,  which  has  been  already  described.  This 
parallax  of  a  heavenly  body  is  the  angle  which  the  mean 
distance  of  the  earth  from  the  snn  subtends  when  seen 
from  the  body.  The  distance  of  the  body  from  the  sun  is 
inversely  as  the  parallax  (nearly).  Thus  the  mean  distr:  ^9 
of  Saturn  being  9.5,  its  annual  parallax  exceeds  6°,  while 


t 


i 


816 


ASTUOyoitY. 


that  of  Neptune,  which  is  three  times  as  far,  is  about  2*^. 
It  was  very  evident,  without  telescopic  observation,  that 
the  stars  could  not  have  a  parallax  of  one  half  a  degree. 
They  must  therefore  be  at  least  twelve  times  as  far  as 
Saturn  if  the  Copernican  system  were  true. 

When  the  telescope  was  applied  to  measurement,  a  con- 
tinually increasing  accuracy  began  to  be  gained  by  the 
improvement  of  the  instruments.  Yet  for  several  genera- 
tions the  parallax  of  the  fixed  stars  eluded  measurement. 
Very  often  indeed  did  observers  think  they  had  detected 
a  parallax  in  some  of  the  brighter  stars,  but  their  succes- 
sors, on  re})eating  their  measures  with  better  instruments, 
and  investigating  their  methods  anew,  found  their  conclu- 
sions erroneous.  Early  in  the  present  century  it  became 
certain  that  even  the  brighter  stars  had  not,  in  general,  a 
parallax  as  great  as  1',  and  thus  it  became  certain  that  they 
must  lie  at  a  greater  distance  than  200,000  times  that 
which  separates  the  earth  from  the  sun. 

SuooetBs  in  actually  measuring  the  parallax  of  the  stars 
was  at  length  obtained  almost  simultaneously  by  two  as- 
tronomers, BsssELof  Kdnigsbergand  STRUVE'of  Dorpat. 
Bessel  selected  61  Cfygni  for  observation,  in  August,  1837. 
The  result  of  two  or  three  years  of  observation  was  that 
this  star  had  a  parallax  of  0'.35,  or  about  one  third  of  a 
second.  This  would  make  its  distance  from  the  sun  nearly 
600,000  astronomical  units.  The  reality  of  this  parallax 
has  been  well-established  by  subsequent  investigators,  only 
it  has  been  shown  to  be  a  little  larger,  and  therefore  the 
star  a  little  nearer  than  Bessel  supposed.  The  most  prob- 
able parallax  is  now  found  to  be  0'.51,  corresponding  to  a 
distance  of  400,000  radii  of  the  earth's  orbit. 

The  distances  of  the  stars  are  sometimes  expressed  by 


1C8  as  far,  is  about  2*^. 
sopio  observation,  tlmt 
:  of  Olio  hulf  a  degree, 
welve  times  as  fur  ob 
iro  true. 

0  measurement,  a  con- 
to  be  gained  by  the 

Yet  for  several  genera- 
eluded  measurement, 
ink  tbcy  had  detected 
stars,  but  their  succes- 
ith  better  instruments, 
w,  found  their  conclu- 
ciit  century  it  became 
hud  not,  in  genera),  a 
Bcame  certain  that  they 
,n  200,000  times  that 
lun. 
purulhix  of  the  stars 
ultaneonsly  by  two  as- 
nd  STRUVE'of  Dorpat. 
ation,  in  August,  1837. 

1  observation  was  that 
about  one  tliird  of  a 

ce  from  the  sun  nearly 
eality  of  this  parallax 
ent  investigators,  only 
ger,  and  therefore  the 
oscd.  The  most  prob- 
51,  corresponding  to  a 
It's  orbit 
>metime8  expressed  by 


MOTIONS  AND  DISTANCES  OF  THE  STAltS.      317 

the  time  required  for  light  to  pass  from  them  to  our  sys- 
tem. The  velocity  of  light  is,  it  will  be  remembered,  about 
300,000  kilometres  per  second,  or  such  as  to  pass  from  the 
sun  to  the  earth  in  8  minutes  18  seconds. 

The  time  required  for  light  to  reach  the  earth  from  some 
of  the  stars,  of  which  the  parallax  has  been  measured,  is  as 
follows : 


8*Am. 

a  Oentauri 

61  C^gni. ...... 

21.185  Lelande.. 

fi  Centauri 

ft  Catnoptia 

84  Oroomliridec 
21,258  Lelande.. 
17.415  Oeltzvn.. 

SirivM 

a  Lyra 


Ymh. 

8-5 

6-7 

6-8 

«.9 

9-4 

10-5 

119 

181 

10. 7 
17-9 

Stab. 

70  Ophiuehi 

t  UrMB  Mtijorit 

Areturuii 

y  Draeoni* 

ItiaOOroombndge. 

Patarit 

8077  Brndky 

85  llegoM 

a  Auriga 

6  Draeoni* 


YMurt. 


191 
24-8 
25-4 
85-1 
85-9 
42-4 
401 
64-5 
70- 1 
129- 1 


OHAl»TER  VI. 
CONSTRUCTION   OF  THE   HEAYENa 

The  visible  uniTerae,  as  revealed  to  us  by  the  telescope,  ia 
a  collection  of  many  millions  of  stars  and  of  several  thon- 
sand  nebnlae.  It  is  sometimes  called  the  stellar  or  sidereal 
system,  and  sometimes,  as  already  remarked,  the  stellar 
universe.  The  most  far-reaching  question  with  which 
astronomy  has  to  deal  is  that  of  the  form  and  magnitude 
of  this  system,  and  the  arrangement  of  the  stars  which 
compose  it. 

It  was  once  supposed  that  the  stars  were  arranged  on  the 
same  general  plan  as  the  bodies  of  the  solar  system,  being 
divided  up  into  great  numbers  of  groups  or  clusters,  while 
all  the  stars  of  each  group  revolved  in  regular  orbits  round 
the  centre  of  the  group.  All  the  groups  were  supposed  to 
revolve  around  some  great  common  centre,  which '  was 
therefore  the  centre  of  the  visible  universe. 

But  there  is  no  proof  that  this  view  is  correct  We  have 
already  seen  that  a  great  many  stars  are  collected  into  clus- 
ters, but  there  is  no  evidence  that  the  stars  of  these 
dusters  revolve  in  regular  orbits,  or  that  the  dusters  them- 
selves have  Any  regular  motion  around  a  common  centra. 

The  lint  Mtmnomer  to  make  a  canf  ul  study  of  the  amngeawnt 
of  the  atara  with  a  view  to  learn  the  atnicture  of  the  heavena  was  Sir 
WtUAJM  HsiiaciRL. 

HsBacmBL's  method  of  atiidy  waa  founded  on  a  mode  of  observo. 


Hi 


;  VI. 

THE   HEAVEN& 

Bd  to  UB  by  the  telescope,  is 
stars  and  of  several  thon- 
alled  the  stellar  or  sidereal 
lady  remarked,  the  stellar 
ing  qncstion  with  which 
the  form  and  magnitade 
sment  of  the  stars  which 

stars  were  arranged  on  the 
of  the  solar  system,  being 
f  groups  or  clasters,  while 
red  in  regular  orbits  ronnd 
e  gronps  were  sapposed  to 
nmon  centre,  which '  was 
B  nniverse. 

view  is  correct    We  have 

tars  are  collected  into  dns- 

that  the  stars  of  these 

or  that  the  clasters  thom- 

ronnd  a  common  centre. 

»f  ul  study  of  the  amngenwiit 
nictura  of  the  heayena  wm  Sir 


ounded  on  a  mode  of  observa- 


COHSTRUCTIOy  OF  THE  HKA  VEHS.  319 

lion  which  ho  CBlIci  targauaing.  It  consinloil  in  polnling  a  power- 
ful lelescope  low.ml  varloun  purl-  of  lliu  hcuveiis  uuil  '"H^^t.rl.ai.lng  by 
..climl  count  liow  thick  the  sturn  were  in  lucli  regicu.  M  s  aOToot 
rorteclorwas  provi.kd  wHli  such  iii.  eyepiece  timi  in  looking  Into 
il  ho  woulil  see  a  porliou  t)f  tlie  heavens  ..Imut  15  in  di.inieler.  A 
circle  of  this  si7*  on  lh«  celcMl..!  sph.ro  has  uh..ut  one  quarter  ho 
apparent  surface  of  ihe  sun.  or  «f  the  full  n«Hni.  On  Hmlng  tho 
ulwpo  in  any  direction,  a  greater  <.r  le«  number  of  stars  were 
nearly  always  visible.  Tbc^c  were  counted,  and  ilio  direction  in 
which  the  telesa.pe  pointed  was  noted.  Gauges  of  this  kind  were 
inado  in  all  parU  of  the  sky  at  wliich  Im  could  |H>int  his  instrument, 
and  the  result*  were  tabulated  in  Ihe  order  of  right  ascension. 

Tho  following  Is  an  extract  from  the  gauges,  an.l  gives  the  average 
number  of  stars  in  each  lleUl  at  tho  p«»lnlH  noted  in  right  aKcnsion 
and  uorlh-p«>lar  distance: 


a  A 

N.  p.  D. 

W  to  W. 

No.  of  sun. 

RA. 

N.  P.  D. 

7B»toW. 

No.  or  SUuu 

h. 
15 

in 

16 
16 

m. 
10 
47 

an 

87 

9.4     • 

10.6 
18.6 
18.6 

h.l 
11 

Vi 

\l 

14 

44 
4V 

8.1 
4.6 
8.9 
8V« 

In  UiU  small  Uible.  It  Is  plain  that  a  diffctenl  law  of  clustering  or 
of  distrlbiitlon  obtains  in  llie  two  regions. 

The  number  of  these  stars  in  certain  portions  is  very  great,  ror 
example.  In  the  Milky  Way  tids  number  was  as  great  as  116.000  stars 
In  a  quarter  of  an  hour  In  some  cases.  ...       ,   , 

Hkmchei.  supposed  at  ftrst  tliat  he  completely  resolvetl  tho  whole 
Milky  Way  Into  smalt  stom.    ThU  conclusion  he  subsequently  modi- 

"It  Is  very  probable  that  the  great  stratum  called  the  Milky  Way  Is 
tint  In  which  the  sun  is  placed,  though  perhaps  not  In  the  very  cen- 
tre of  iu  Ihickneaa.  _  ,  . ,  , 

••  We  gather  Ibis  from  the  appearance  of  ibe  Gidaxy.  which  seems 
to  encompass  the  whole  heavens,  as  it  certainly  must  »lo  if  the  sun  la 
wltb'n  It.  For.  suppose  a  number  of  stars  arranged  between  two 
parallel  plane*,  indefinitely  extended  every  way.  but  at  a  given  con- 
siderable distance  from  each  other,  and  calling  this  a  sidereal  stratum, 
nn  eye  placed  wiewUere  wHWu  H  will  sge  all  tUe  stars  in  the  dlrw 


J» 


MiST'" 


810 


A8TR0N0MT. 


'   '4  i 


lion  of  the  planes  of  tlie  stratiiin  projected  into  n  grcnl  ciiclv,  wlileh 
will  appear  lucid  on  account  of  (lie  accumulation  of  llie  Hiars,  wkilr 


L 


Ik 


*  f 


•'  T   '    . 

♦    f  1  1.; 

»    f .!  > ' 

,  •*■  y, 


Fio.  9S.— HBUOHn'a  Trjomt  or  the  SmxAa  Sthsm. 

the  rest  of  the  heavens,  at  tlie  sides,  will  only  Fecm  to  be  fcnttcred 
orer  with  constellations,  more  or  less  crowded.  ac<;ording  to  the  dls- 


ifiiiii' iiiiwiiiii  miiwi 


rr. 


CONSTRUCTION  OF  TIIK  IIK.WKNS. 


331 


l«l  Into  n  grent  tiiclc,  which 
umulation  of  the  Hiars,  while 


■Hx  Srcuum  Stmsm. 

ill  only  Fecm  to  be  ccnttcred 
Dw^ed,  iic<;ordlng  to  the  dig- 


tsncc  of  tlio  plnnes.  or  number  of  Mnr«  contained  in  Uic  thitknoM  or 
siiieH  of  tlie  Rtratum." 

Th«»  in  Hkrschki.'h  tigure  im  wyciU  S  within  the  Htrnlum  <tb  will 
Rco  the  star*  in  the  liircclloii  of  its  length  ab.  or  height  erf.  wllli  nil 
those  In  the  iiitermpainte  HitunlionH,  projttletl  into  the  lucid  circle 
A  CU  D,  Willie  those  in  tlie  sides  m  r.  n  w.  will  be  seen  scattered  over 
the  remnining  purt  of  the  iieavens  M  VN  W. 

"  If  the  eye  were  plnced  somewhere  williout  the  stratum,  at  no 
very  grent  distance,  the  uppearnnce  of  the  stars  within  it  would 
assume  the  form  of  one  of  the  smaller  circles  of  the  sphere,  which 
would  be  more  or  less  contracted  acconling  to  the  distance  of  the 
eye;  and  If  this  distance  were  exceedingly  lncrea«c<l.  Iho  whole 
stratum  might  at  Inst  be  drawn  together  into  a  lucid  spot  «>f  any 
slinpe.  according  to  the  length,  brcadili,  and  height  of  the  stratum. 

"  Suppose  that  a  smaller  stratum  pq  sliould  branch  out  from  ihe 
former  in  a  certain  «lircclion,  and  tiiat  it  also  is  contained  lietwccn 
two  puraiiel  planes,  so  that  Iho  eye  is  contidned  wiiliin  the  great 
stratum  soniewliere  Itefore  the  separation,  and  not  far  from  llie  place 
where  lliu  stnila  are  still  unitetl.  Then  tills  second  stratum  will  not 
lie  piojeeled  into  a  brijthl  circle  like  the  former,  but  it  will  be  «?en 
as  a  lucid  branch  pKM-ewling  from  the  first,  and  returning  into  it 
again  at  a  distance  less  than  a" semicircle. 

"In  the  tigure  liic  stars  in  Ihe  small  stratum  p?  will  be  projectwl 
into  a  bright  arc  riitt  P.  which,  after  Its  separation  from  llie  circle 
CBD,  unites  with  it  again  at  I\ 

"If  tlie  iKiuiKling  surfan-s  are  not  parallel  planes,  but  irregidarly 
curved  surfacc-s.  anulogoiis  appearances  must  result." 

The  Milky  Way.  as  we  see  it  with  the  naked  eye,  presents  the 
as|M>ct  which  has  liecn  Just  accounted  for.  in  Its  general  appearance 
of  a  girdle  around  the  heavens  and  in  its  bifurcation  at  a  certain 
point,  and  Heiuchei.'8  explanation  of  this  appearance,  as  Just  given, 
has  never  been  seriously  qucstionwi.  One  doubtful  point  remains: 
are  the  stars  in  Pig.  IW  scattered  all  through  the  space  8—abpd1 
or  are  they  near  its  bounding  planes,  or  clustered  in  any  way  wHhln 
this  space  so  as  to  produce  the  same  result  to  the  eye  as  If  uniformly 
distributed  T 

HBRacHBi.  assumed  that  they  were  nearly  equably  arranged  all 
through  the  space  in  question.  He  only  examined  one  other  arrange- 
ment—viz., tbiit  of  a  ring  of  stars  surrounding  the  sun— and  he  pro- 
nouuce«l  against  auch  an  arrangement,  for  the  reason  that  tiiere  is 
absolutely  nothing  in  the  slxe  or  brilliancy  of  the  sun  to  cause  us  to 
suppose  It  to  be  the  centre  of  such  a  gigantic  system.  No  reason  ex- 
cept its  Importauce  to  us  personally  can  be  alleged  for  such  a  sup- 


832 


ASTHOAOMy. 


potitinn.  By  llio  nMiimptloni  of  Vlij.  «8,  cai  li  titur  will  Imve  ill 
own  rippcarnniti  of  n  paiiixy  or  milky  wny.  wlilcli  will  viiiy  nccoid- 
ttiff  to  ilio  Nituatinn  of  lliu  Nliir. 

Such  an  rxpltumtioii  will  nccouiit  for  llie  general  nppenrnnciH  of 
the  Milky  Way  iiudof  the  rent  of  the  iiky.  ■uppo«inKllicatiirNci|ually  or 
nearly  equally  «liitrll»uled  in  8piice.  On  thin  auppoflilion,  the  lyitcm 
muat  be  ilee|>er  wliciv  the  »lur»  appear  mure  niimvroui. 


..-s^ammm 


V\fi.  08,  cui'li  Hlur  will  Imve  lit 
y  wny.  wlikli  will  viiry  nccoid- 

for  llie  general  appcnronceH  of 
ky,  RiipponinK  »■«  •tiirH  eiiually  or 
On  tliis  auppoiilion,  tlie  lyitein 
ur  more  numuroiii. 


CHAPTER  VII. 


COSMOGONY. 

A  THEORY  of  the  o|.,ration8  by  which  the  universe  re- 
ceived it8  present  form  and  arrangement  is  called  Cosmog- 
ony. Thia  subject  does  not  treat  of  the  origin  of  matter, 
but  only  of  its  trunaformations. 

Three  systems  of  Cosmogony  have  prevailed  among 
thinking  men  at  different  times: 

(1)  That  the  universe  had  no  origin,  but  existed  from 
eternity  in  the  form  in  which  we  now  see  it.  This  was  the 
view  of  the  ancient  philosophers. 

(2)  That  it  was  created  in  its  present  shape  in  a  mo- 
ment, out  of  nothing.  This  view  is  based  on  the  literal 
sense  of  the  words  of  the  Old  Testament. 

(3)  That  it  came  into  its  present  form  through  an  ar- 
rangement of  materials  which  were  before  "  without  form 
and  void."  This  may  be  called  the  evolution  theory.  It 
is  to  be  noticed  that  no  attempt  is  made  to  explain  the 
origin  of  the  primitive  matter. 

The  last  is  the  idea  which  has  prevailed,  and  it  receives 
many  striking  confirmations  from  the  scientific  discoveries 
of  modem  times.  The  latter  seem  to  show  beyond  all  rea- 
sonable doubt  that  the  universe  could  not  always  have 
existed  in  its  present  form  and  under  its  present  condi- 
tions ;  that  there  was  a  time  when  the  materials  composing 
it  were  masses  of  glowing  vapor,  and  that  there  will  be  a 


«# 


.;!^:  yl 


324 


ASTRONOMY. 


time  when  the  present  state  of  things  will  cease.  The  ex- 
planation of  the  processes  through  Avhich  this  occurs  is 
sometimes  called  the  nebular  hypothesis.  It  waa  first  pro- 
pounded by  the  philosophers  Swedenborg,  Kant,  and 
Laplace,  and,  although  since  greatly  modified  in  detail, 
their  views  have  in  the  main  been  retained  until  the 
present  time. 

We  shall  begin  its  consideration  by  a  statement  of  the 
various  facts  which  appear  to  show  that  the  earth  and 
planets,  as  well  as  the  sun,  were  once  a  fiery  mass. 

The  first  of  these  facts  is  the  gradual  but  uniform  in- 
crease of  temperature  as  we  descend  into  the  interior  of 
the  earth.  Wherever  mines  have  been  dug  or  wells  sunk 
to  a  great  depth,  the  temperature  increases  as  we  go  down- 
ward at  the  rate  of  about  one  degree  centigrade  to  every  30 
metres,  or  one  degree  Fahrenheit  to  every  50  feet.  The 
rate  differs  in  different  places,  but  the  general  average  ic 
near  this.  The  conclusion  which  we  draw  from  this  may 
not  at  first  sight  be  obvious,  because  it  may  seem  that  the 
earth  might  always  have  shown  this  same  increase  of  tem- 
perature. But  there  are  aeveral  results  which  a  little 
thouglit  will  make  clear,  a'Luough  their  complete  establish- 
ment requires  the  use  of  the  higher  mathematics. 

The  first  result  is  that  the  increase  of  temperature  can- 
not be  merely  superficial,  but  must  extend  to  a  great 
depth,  probably  even  to  the  centre  of  the  earth.  If  it  did 
not  so  extend,  the  heat  would  have  all  been  lost  long  ages 
ago  by  conduction  to  the  interior  and  by  radiation  from 
the  surface.  It  is  certain  tliat  the  earth  has  not  received 
any  great  supply  of  heat  from  outside  since  the  earliest 
geological  ages,  because  such  an  accession  of  heat  at  the 
earth's  earface  wonld  have  destroyed  all  life,  and  even 


f.1^;^'.-rT'>"'-".^>-fr\'V^.**-'*^''S'T*>^<-^ "'"«"■  ■•' -^^v-^JbV''- 


COSMOGONY. 


325 


gs  will  cease.  The  ex- 
li  Avliich  this  occurs  is 
hesis.  It  waa  first  pro- 
DENBORG,  Kant,  and 
itly  modified  in  detail, 
!en  retained  until  the 

bj  a  statement  of  the 
)w  that  the  earth  and 
ce  a  fiery  mass, 
radual  but  uniform  in- 
id  into  the  interior  of 
seen  dug  or  wells  sunk 
icreases  as  we  go  down- 
;  centigrade  to  every  30 
to  every  50  feet.  The 
the  general  average  k 
c  draw  from  this  may 
B  it  may  seem  that  the 
i  same  increase  of  tcm- 
results  which  a  little 
leir  complete  cstablish- 
mathematics. 
ise  of  temperature  can- 
ist  extend  to  a  great 
>f  the  earth.  If  it  did 
all  been  lost  long  ages 
and  by  radiation  from 
earth  has  not  received 
fiide  since  the  earliest 
scession  of  heat  at  the 
fed  all  life,  and  even 


melted  all  the  rocks.  Therefore,  whatever  heat  there  is 
in  the  interior  of  the  earth  must  have  been  there  from  be- 
fore the  commencement  of  life  on  the  globe,  and  remained 
through  all  geological  ages. 

The  interior  of  the  earth  being  hotter  than  its  surface, 
and  hotter  than  the  space  around  it,  must  be  losing  heat. 
We  know  by  the  most  familiar  observation  that  if  any  ob- 
ject is  hot  inside,  the  heat  will  work  its  way  through  to  the 
surface  by  the  process  of  conduction.  Therefore,  since  the 
earth  is  a  great  deal  hotter  at  the  depth  of  30  metres  than 
it  is  at  the  surface,  heat  must  be  continually  coming  to  the 
surface.  On  reaching  the  surface,  it  must  be  radiated  oft 
into  space,  else  the  surface  would  have  long  ago  become 
as  hot  as  the  interior.  Moreover,  this  loss  of  heat  must 
have  been  going  on  since  the  beginning,  or  at  least  since 
a  time  when  the  surface  was  as  hot  as  the  interior.  Thus,  if 
we  reckon  backward  in  time,  we  find  that  there  must  have 
been  more  and  more  heat  in  the  earth  the  further  back 
we  go,  so  that  we  must  finally  reach  back  to  a  time  when 
it  was  80  hot  as  to  be  molten,  and  then  again  to  a  time 
when  it  was  so  hot  as  to  be  a  mass  of  fiery  vapor. 

The  second  fact  is  that  we  find  the  sun  to  be  cooling  off 
like  the  earth,  only  at  an  incomparably  more  rapid  rate. 
The  sun  is  constantly  radiating  heat  into  space,  and,  so  far 
as  we  can  ascertain,  receiving  none  back  again.  A  small 
portion  of  this  heat  reaches  the  earth,  and  on  this  portion 
depends  the  existence  of  life  and  motion  on  the  earth's  sur- 
face. The  quantity  of  heat  which  strikes  the  earth  is  only 
about  TTinn^innr  «'  tl^*'  which  the  sun  radiates.  This 
fraction  expresses  the  ratio  of  the  apparent  surface  of  the 
earth,  as  seen  from  the  sun,  to  that  of  the  whole  celestial 
Inhere. 


1^ 


m 


326 


ASTRONOMY. 


m:^ 


m^^ 


Since  the  Bun  is  losing  beat  at  this  rate,  it  must  have  had 
more  heat  yesterday  than  it  has  to-day ;  more  two  days  ago 
than  it  had  yesterday,  and  so  on.  Thus  culculating  back- 
ward, we  find  that  the  further  wo  go  back  into  time  the 
hotter  the  sun  must  have  b^en.  Since  we  know  that  heat 
expands  all  bodies,  it  follows  that  the  sun  must  have  been 
larger  in  past  ages  than  it  is  now,  and  we  can  trace  back 
this  increase  in  size  without  limit.  Thus  we  are  led  to  the 
conclusion  that  there  must  hare  been  a  time  wlien  the  sun 
filled  up  the  space  now  occupied  by  the  planets,  and  muat 
have  been  a  very  rare  mass  of  glowing  vapor.  The  plan- 
ets could  not  then  have  existed  separately,  but  must  have 
formed  a  part  of  this  mass  of  vapor.  The  latter  was  there- 
fore the  material  out  of  which  the  solar  system  was 
formed. 

Tho  same  process  may  bo  continued  into  the  future. 
Since  the  sun  by  its  radiation  is  const  mf:  Voing  heat,  it 
must  grow  cooler  and  cooler  as  ages  ai  ,.  -^,  and  must 
finally  radiate  so  little  heat  that  life  anc  ::  ...^.lon  can  no 
longer  exist  on  our  globe. 

The  third  fact  is  that  the  revolutions  of  all  the  planets 
around  the  sun  take  place  in  the  same  direction  and  in 
nearly  the  same  plane.  We  have  here  a  similarity  amongst 
the  different  bodies  of  the  solar  system,  which  must  have 
had  an  adequate  cause,  and  the  only  cause  which  has  ever 
been  assigned  is  found  in  the  nebular  hypothesis.  This 
hypothesis  supposes  that  the  snn  and  planets  were  once 
a  great  mass  of  vupor,  as  large  as  or  larger  than  the  present 
solar  system,  revolving  on  its  axis  in  the  same  plane  in 
which  the  planets  now  revolve. 

The  fourth  fact  is  seen  in  the  existence  of  nebulae.  The 
spectroscope  shows  these  bodies  to  be  masses  of  glowing 


..isga^asgag^s^a 


I  rate,  it  must  have  had 
ay ;  more  two  days  ago 
rims  calculating  back- 
go  back  into  time  the 
ice  we  know  that  heat 
lie  snn  must  have  been 
and  we  can  trace  back 
Thus  we  are  led  to  the 
in  a  time  when  the  sun 
the  planets,  and  muat 
ring  vapor.  The  plan- 
arately,  but  must  have 
The  latter  was  thcre- 
the  solar   system  was 

nned  into  the  future. 
msi  viit:  looing  heat,  it 
res  ai  V.  .\  and  must 
fe  anc  i.^jion  can  no 

itions  of  all  the  planets 
same  direction  and  in 
;re  a  similarity  amongst 
stem,  which  must  have 
ly  cause  which  has  ever 
ular  hypothesis.  This 
and  planets  were  once 
larger  than  the  present 
I  in  the  same  plane  in 

stence  of  nebulae.  The 
>  be  masses  of  glowing 


COSMOGONY. 


837 


vapor.    We  thus  actually  see  matter  in  the  celestial  spaces 
under  the  very  form  in  which  the  nebular  hypothesis  sup- 
poses the  matter  of  our  solar  system  to  have  once  existed. 
Since  these  masses  of  vapor  are  so  hot  as  to  radiate  light 
and  heat  through  the  immense  distance  which  separates  us 
from  them,  they  must  be  gradually  cooling  off.    This  cool- 
ing  must  at  length  reach  a  point  when  they  will  cease  to 
be"  vaporous  and  condense  into  objects   like  stars    and 
planets.    We  know  that  every  star  in  the  heavens  radiates 
heat  as  our  sun  does.     In  the  case  of  the  brigliter  stars  the 
heat  radiated  has  been  made  sensible  in  the  foci  of  our 
telescopes  by  means  of  the  thermo-multiplier.    All  the 
stars  must,  like  the  sun,  be  radiating  heat  into  space. 

A  fifth  fact  is  afforded  by  the  physical  constitution  of 
the  planets  Jupiter  and  Saturn.  The  telescopic  examina- 
tion of  these  planets  shows  that  changes  on  their  surfaces 
are  constantly  going  on  with  a  rapidity  and  violence  to 
which  nothing  on  the  surface  of  our  earth  can  compare. 
Such  operations  can  be  kept  up  only  through  the  agency  of 
heat  or  some  equivalent  form  of  energy.  But  at  the  dis- 
tance of  Jupiter  and  Saturn  the  rays  of  the  sun  are  entirely 
insufficient  to  produce  changes  so  violent.  We  are  there- 
fore led  to  infer  that  Jupiter  and  Saturn  must  be  hot 
bodies,  and  must  therefore  be  cooling  off  like  the  sun, 

stars,  and  earth. 

We  are  thus  led  to  the  general  conclusion  that,  so  far 
as  our  knowledge  extends,  nearly  all  the  bodies  of  the 
universe  are  hot,  and  are  cooling  off  by  radiating  their 

heat  into  space. 

The  idea  that  the  heat  radiated  by  the  sun  and  stars  may 
in  some  way  be  collected  and  returned  to  them  by  the 
operation  of  known  natural  laws  is  equally  untenable.    It 


il 


•{- 


8S8 


ASTRONOiir. 


m 


m\ 


iH  a  fundumental  principle  of  the  laws  of  heat  that  "  the 
hitter  ciiii  never  pass  from  u  cooler  to  a  warmer  body,'*  and 
that  a  body  can  never  grow  warm  or  acquira  heat  in  a  space 
that  is  cooler  than  the  body  is  itself.  All  differences  of 
temperature  tend  to  eciualixe  themselves,  and  the  onl/ 
state  of  things  to  which  the  universe  can  tend,  under  its 
present  laws,  is  one  in  which  all  space  and  all  the  bodies  con- 
tained in  space  ure  at  a  uniform  tem]ieratnre,  and  then  all 
motion  and  change  of  tem])erature,  and  hence  the  condi- 
tions of  vitality,  must  cease.  And  then  all  such  life  as  ours 
must  cease  also  unless  sustained  by  entirely  new  methods. 

The  general  result  drawn  from  all  these  laws  and  facts 
is,  that  there  was  once  a  time  when  all  the  bodies  of  the 
universe  formed  either  a  single  mass  or  a  number  of  masses 
of  fiery  vapor,  having  slight  motions  in  various  parts,  and 
different  degrees  of  density  in  different  regions.  A  grad- 
ual condensation  around  the  centres  of  greatest  density  then 
went  on  in  consequence  of  the  cooling  and  the  mutual  at- 
traction of  the  parts,  and  thus  arose  a  great  number  of 
nebulous  masses.  One  of  these  masses  formed  tlie  ma- 
terial out  of  which  the  sun  and  planets  arc  supposed  to 
have  been  formed.  It  waa  probably  at  first  nearly  glob- 
ular, of  nearly  equal  density  throughout,  and  endowed 
with  a  very  slow  rotation  in  the  direction  in  which  the 
planets  now  moTC.  As  it  cooled  OiT,  it  grew  smaller  and 
smaller,  and  its  velocity  of  ruUition  increased  in  rapidity. 

The  rotating  mass  we  have  described  must  have  had  an  axis 
around  which  it  rotated,  and  therefore  an  equator  defined 
88  being  everywhere  00°  from  this  axis;  In  consequence 
of  the  increase  in  the  velocity  of  rotation,  the  centrifugal 
force  would  also  be  increased  as  the  mass  grew  smaller. 
This  force  varies  as  the  radius  of  the  circle  described  by 


COSMOOONT. 


329 


i\v8  of  heat  that  "  the 
)  a  Wanner  body,"  and 
acquii'c  heat  in  a  space 
!lf.  All  diffci-ences  of 
nselves,  and  the  onl/ 
se  can  tend,  under  its 

I  and  all  the  bodies  con- 
jieratnre,  and  then  all 

and  hence  the  condi- 
lien  all  snch  life  as  ours 
entirely  new  methods. 

II  these  laws  and  facts 
1  all  the  bodies  of  the 
or  a  number  of  masses 
s  in  various  parts,  and 
•ent  regions.  A  grad- 
>f  greatest  density  then 
ngand  the  mutual  at- 
>se  a  great  number  of 
asses  formed  tlie  mo- 
lanets  arc  supposed  to 
y  at  first  nearly  glob- 
ughont,  and  endowed 
irection  in  which  the 
u,  it  grew  smaller  and 

increased  in  rapidity. 
i  most  have  had  an  axis 
ore  an  equator  defined 
axis.  In  consequence 
tation,  the  centrifugal 
10  mass  grew  smaller. 
:he  circle  described  by 


any  particle  multiplied  by  the  square  of  its  angular  velocity. 
Hence  when  the  masses,  being  reduced  to  half  the  rrnlnis, 
rotated  four  times  as  fust,  the  centrif ugal  force  at  the  equa- 
tor would  be  increased  ix4',  or  eight  times.    The  gravi- 
tation of  the  ma83  at  the  surface,  ocing  inversely  as  the 
square  of  the  distance  from  the  centre,  or  of  the  radius, 
would  bo  increased  four  times.     Thorofcio  as  the  masses 
continue  to  contract,  the  centrifugal  force  increases  at  a 
more  rapid  rate  than  the  central  attraction.     A  tunc  ^vould 
therefore  come  when  they  would  balance  each  other  at  the 
equator  of  the  mass.    Tbe  mass  would  then  cease  to  con- 
tract at  the  equator,  but  at  the  poles  there  would  be  no 
centrifugal  force,  and  the  gravitation  of  the  mass  would 
grower  stronger  and  stronger.    In  consequence  the  mass 
would  at  length  assume  the  form  of  a  lens  or  disk  very  thm 
in  proportion  to  its  extent.    The  denser  portions  of  this 
lens  would  gradually  be  drawn  toward  the  centre,  and  there 
more  or  less  solidified  by  the  process  of  cooling     A  point 
would  at  length  be  reached,  when  solid  particles  would  begin 
to  be  formed  throughout  the  whole  disk.    Tliese  would  grad- 
ually condense  around  each  other  and  form  a  single  planet,  or 
they  might  break  up  into  small  masses  and  form  a  group  of 
planets.    As  the  motion  of  rotation  would  not  be  altered 
by  these  processes  of  condensation,  these  planets  would  all 
be  rotating  around  the  central  part  of  the  mass,  which  is 
supposed  to  have  condensed  into  the  sun. 

It  is  supposed  that  at  first  those  planetary  masses,  being 
very  hot,  were  composed  of  a  central  mass  of  those  sub- 
stances which  condensed  at  a  very  hi-h  temporatnre,  sur- 
rounded bv  the  vapors  of  those  substances  which  were 
more  volatile.  We  know,  for  instance,  that  it  takes  a  much 
higher  temiwaturc  to  reduce  lime  and  platinum  to  vapor 


:it 


330 


ASTRONOMT. 


tluin  it  does  to  reduce  iron,  zinc,  or  magnesium.  There- 
fore,  in  tlio  original  planets,  the  limes  and  earths  would 
condense  first,  while  many  other  metals  would  still  bo  in 
a  state  of  vapor.  The  planetary  masses  would  each  bo 
afFccted  by  a  rotation  increasing  in  rapidity  as  thiy  grew 
smaller,  and  would  at  length  forpi  masses  of  melted  metals 
and  vapors  in  the  same  way  as  the  larger  mass  out  of  which 
the  sun  and  planets  were  formed.  These  masses  would 
then  condense  into  a  planet,  with  satellites  revolving 
around  it,  just  as  the  original  mass  condensed  into  sun  and 
)>lanct8. 

At  first  the  planets  would  be  so  hot  its  to  bo  in  a  molten 
condition,  each  of  them  probably  shining  like  tho  sun. 
They  would,  however,  slowly  cool  off  by  the  radiation  of 
heat  from  their  surfaces.    So  long  as  they  remained  liquid, 
the  surface,  as  fast  as  it  grew  cool,  would  sink  into  the  in- 
terior on  account  of  its  greater  specific  gravity,  and  its 
place  would  bo  taken  by  hotter  material  rising  from  the 
interior  to  the  sarfaoe,  there  to  cool  off  in  its  turn.    There 
would,  in  fact,  be  a  motion  something  like  tJmt  which 
occura  when  a  pot  of  ccld  water  is  set  upon  the  fire  to  boil. 
Whenever  a  mass  of  water  at  the  bottom  of  the  pot  ii 
lieated,  it  rises  to  the  surface,  and  the  cool  water  moves 
down  to  take  its  place.     Thus,  on  the  whole,  so  long  as 
tho  planet   remained  liquid,  it  would   cool  off  equally 
throughout  its  whole  mass,  owing  to  the  constant  motion 
from  tho  centre  to  tho  circumference  and  back  again.    A 
time  would  at  length  arrive  when  many  of  the  earths  and 
metals  would  begin  to  solidify.    At  fii-st  the  solid  particles 
would  be  carried  up  and  down  with  the  liquid.    A  time 
would  finally  arrive  when  they  would  become  so  large 
and  numerous,  and  tho  liquid  part  of  tho  general  mass 


-■^■■i?!;'^g!g«r';#lfeteA.^^<^ 


iMte-. 


COSMOGONY. 


881 


r  magnesium.  There- 
IHC8  and  earths  would 
stals  would  still  bo  in 
nusses  would  each  bo 
rapidity  as  thiy  grew 
lasses  of  melted  metuls 
rger  mass  out  of  which 
These  masses  would 
h  satellites  revolving 
ondensed  into  sun  and 

)t  as  to  bo  in  a  molten 
shining  like  the  sun. 
»flf  by  the  radiation  of 

they  remained  liquid, 
ould  sink  into  the  in- 
scific  gravity,  and  its 
terial  rising  from  the 
>fl  In  its  turn.  There 
hing  like  Umt  which 
t  upon  the  lire  to  boil, 
bottom  of  the  pot  ji 
the  cool  water  moves 
bhe  whole,  so  long  as 
raid  cool  off  equally 
)  the  constant  motion 
)  and  back  again.  A 
any  of  the  earths  and 
irat  the  solid  particles 

the  liquid.    A  time 
uld  become  so  large 

of  the  general  mass 


become  so  viscid,  that  the  motion  would  be  obstructed. 
The  planet  would  then  begin  to  solidify.  Two  views 
have  been  entertained  respecting  the  process  of  solidifica- 
tion. 

According  to  one  view,  the  whole  surface  of  the  planet 
would  solidify  into  a  continuous  wast,  as  ice  forms  over  a 
pond  in  cold  weather,  while  the  interior  was  still  in  a 
molten  state.  The  interior  liquid  i.v.nld  then  no  longer 
come  to  the  sui  m-p  a  cool  off,  and  could  lose  no  heat 
except  what  was  conducted  through  this  crust.  Hence 
the  subsequent  cooling  would  be  much  slower,  and  the 
globe  would  long  remain  a  mass  of  lava,  covered  over  by 
a  comparatively  thin  solid  crust  like  that  on  which  we 

live. 

The  other  view  is  that,  when  the  cooling  attained  a  cer- 
tain stage,  the  centrAl  portion  of  the  globe  would  be 
solidified  by  the  enormous  pressure  of  the  superincumbent 
portions,  while  the  exterior  was  still  fluid,  and  that  thus 
the  solidification  would  take  place  from  the  centre  out- 
ward. 

It  is  still  an  unsettled  question  whether  the  earth  is  now 
solid  to  its  centre,  or  whether  it  is  a  great  globe  lof  molten 
matter  with  a  comparatively  thin  crust.  Asti^mers  and 
physicists  incline  to  the  former  view ;  geologists  to  the  lat- 
ter one.  Whichever  view  may  be  correct,  it  appears  cer- 
tain that  there  are  great  lakes  of  lava  in  the  interior  from 
which  volcanoes  are  fed. 

It  must  be  understood  that  the  nebular  hypothesis,  as  we 
have  explained  it,  is  not  a  perfectly  established  scientific 
theory,  but  only  a  philosophical  conclusion  founded  on  the 
widest  study  of  nature,  and  pointed  to  by  many  otherwise 
disconnected  facts.    The  widest  generalization  associated 


fT 


889 


ASmONOMT. 


PI 


with  it  is  that,  so  fur  us  wo  can  see,  tlic  iiiiivoi'so  is  not  self- 
Bustuining,  but  is  a  kind  ot  orgiini^m  whiuh,  like  all  other 
orgunisms  we  know  of,  nuiat  come  to  an  end  in  consoqncnco 
of  t!..^8e  very  laws  of  action  which  keep  it  going.  It  must 
have  liud  u  beginning  within  a  cortuin  number  of  years 
which  we  cannot  yet  cnlcniute  with  certninty,  but  which 
cannot  mnch  exceed  20,000,000,  and  it  must  end  in  u  chaos 
of  cold,  dead  globes  at  a  calcniable  time  in  the  future, 
when  the  sun  und  stars  ghall  have  radiated  away  all  their 
heat,  unless  it  is  re-creuted  by  the  action  of  forces  of  which 
we  at  present  know  nothing. 


THE  END. 


■n 


ic  iinivoi'BO  is  not  self- 
I  which,  like  all  other 
in  end  in  coiigoqncnco 
op  it  going.  It  mnst 
ain  niimlicr  of  yriirs 

certainty,  but  which 
it  must  end  in  a  chaos 

time  in  the  future, 
idiatod  away  all  their 
ion  of  forces  of  which 


INDEX. 


W-  Thw  Index  Is  iulcndod  to  point  oul  tbe  sul.JccU  trcnlcd  in  the 
work,  nnd  furiher.  to  give  reference-  to  tbe  pnges  where  technical 
terms  are  defined  or  expluined. 


Aberration-constant,    value    oi, 

178. 
Aberration  of  Hglit,  174. 
Achromatic  tclcHCoiJO  descrlbwl, 

68. 
Adams's  work  on  perturbations 

of  Uranus,  250 
Aibt'b  determination  of  the  den- 

aity  of  the  enrtli,  148. 
Algol  (variable  sUr),  296. 
Altitude  of  a  star  defined,  18. 
Angles,  8. 

Annular  eclipses  of  the  sun,  186. 
Apparent  place  of  a  star,  16. 
Apparent  time,  45. 
Abibtarchcs  determines  tlie  so- 
lar parallax,  165. 
Asteroids  defined,  191. 
Asteroids,    numlier   of,  226   in 


Astronomical     Instruments    (in 

general),  60. 
Astronomy  (defined),  1. 
Atmosphere  of  the  moon,  281. 
Atmospheres  of  the  planets,    See 

Mercury,  Venus,  etc. 
Axis  of  the  earth  defined,  21. 
Azimuth  defined,  19. 


Bkbsgi/b  parallax  of  61  Cygnl 

(1887),  816. 
Binary  stars.  802. 
BoDE'ii  law  8tule«l,  198. 
Bond's  discovery  of  the  dusky 

ring  of  Saturn,  1860,250. 
Bouvard's    theory   of  Uranus, 

256. 
Bradley  discovers  aberration  In 

1729.  176. 
Calendars,  how  formed,  182. 
Cassim  discovers  four  satellilcs 

of  Saturn  (1684-1671),  852. 
Catalogues  of  stars,  general  ac- 
count, 79. 
Celestial  sphere,  4  4. 
Centre  of  gravity  of  the  solar 

system,  194. 
Chronology,  180. 
Chronometers,  68. 
Clarke's  elements  of  the  earth, 

152. 
Clocks,  68. 
Clusters  of  stars.  808. 
Comets,  general  account,  274 
Comets'  orbits,  277 
Comets'   tails,    repulsive   force, 
277. 


•4, 


884 


INDEX. 


}'i 


^i-'f 


Comets,  their  phyricnl  constitu- 
tion, 276. 

Comets,  their  spcctrn,  277. 

Conjunction  (of  n  pianet  with 
the  sun)  detlned,  97. 

Consteiltttions,  288. 

Construction  of  tlielieavcn8,817. 

Coordinates  of  a  star  defined, 
1«,  87. 

COPERNICUB,  108. 

Correction  of  a  clock  defined,  BO. 
Cosmogony,  822. 
Corona,  its  spectrum.  216. 
Day,  how  sulMlivided  into  hours, 

etc.,  187. 
Days,  mean  solar  and  solar,  46. 
Declination  of  a  star  defined,  41. 
Distance  of  tlie  fi.ved  stare,  814. 
Distribution  of  the  stars,  818. 
Diurnal  motion,  21,  22. 
Dominical  letter,  186. 
DoNATi'B  comet  (1858),  281. 
Double  (and  multiple)  stars,  801. 
Earth  (the),  general  account  of, 

142. 
Earth's  density,  142. 
Earth's  dimensions,  151. 
Earth's  mass,  142. 
Eclipses  of  the  moon,  181. 
Eclipses  of  the  sun  and  moon, 

129. 
Eclipses  of  the  sun,  explanation, 

182. 
Eclipses  of   tlio   sun,   physical 

phenomena,  212. 
Eclipses,  their  recurrence,  186. 
Ecliptic  defined,  84. 
Elements  of  the  orbito  of  the  ma- 
jor planets,  198. 
Elongation  (of  a  planet)  defined, 
97." 


Encke's  comet,  288. 
Encxk'b  value  of  the  solar  paral- 
lax, 8".578,  166. 
Epicycles,  tlielr  theory,  102. 
Equation  of  time,  188. 
Equator  (celestial)  defined.  21. 
Equntoriui  telescope,  description 

of,  74. 
Equinoxes,  87. 
Eye- pieces  of  telescopes,  62. 
Fabkitius  observes  solar  spots 

(1611).  207. 
Figure  of  the  earlii,  148. 
Future  of  tiic  solar  system,  882. 
Galaxy,  or  milky  way,  819. 
Galileo    olwcrves   solar   spots 

(1611),  207. 
Galileo's  discovery  of  satellites 

of  Jupiter  (1610),  240. 
Galle   first  observes   Neptune 

(1846),  259. 
Geodetic  surveys,  150. 
Golden  number,  184. 
Gravitation  extends  to  the  stars, 

808. 
Gravitation  resides  in  each  par- 
ticle of  matter,  119. 
Gravitation,  terrestrial  (its  laws), 

146. 
Greek  alphabet,  1  *. 
Gregorian  calendar,  185. 
Hallet  predicts  the  return  of  a 

comet  (1682),  279. 
Hall's  discovery  of  satellites  of 

Mars,  285. 
Hansen's  value  of  the  solar  par- 
allax. 8'.92.  166. 
Herschbl  (W.)  discovers  two 
satellites  of  Saturn  (1789),  252. 
Uerschel  (W.)  discovers   two 
satellites  of  Uranus  (1787).  254 


INDKX. 


38R 


[e'b  comet,  388. 

ik'b  yaliie  of  the  lolnr  paral- 

;,  8".578.  166. 

ycles,  their  theory,  103. 

tlion  of  time,  188. 

ttor  (culestini)  tleflned.  31. 

itoriul  telcgci)[)e,  description 

,74. 

Iiioxes,  87. 

pieces  of  telescopes,  63. 

RiTius  observes  solar  spots 

JU),  207. 

ire  of  the  carlli,  148. 

[ire  of  the  solar  system,  883. 

ixy,  or  milky  way,  819. 

,ii,EO    olmerves   solar   spots 

611),  307. 

.ii.Eo'8  discovery  of  satellites 

:  Jupiter  (1610).  340. 

.LE   first  observes   Neptune 

846).  250. 

Kletic  surveys,  150. 

den  number.  184. 

kvitation  extends  to  the  stars, 

08. 

ivitation  resides  in  each  par- 

icle  of  matter,  1 10. 

ivitation,  terrestrial  (its  laws), 

46. 

ioV.  alphabet,  1  *. 

igorian  calendar,  185. 

lLLET  predicts  the  return  of  a 

iomet  (1683),  270. 

iU.'B  discovery  of  satellites  of 

tfars.  385. 

onsen's  value  of  the  solnr  par- 

illnx.  8'.03.  166. 

iiucHBL  (W.)  discovers  two 

Balellites  of  Saturn  (1789),  353. 

CRBCHEii  (W.)  discovers   two 

satellites  of  Uranus  (1787),  254 


IlEB«iiKt(W.)  discovers  Uranus 

(1781).  358. 
Hehsoiibl'b  catalogues  of  nebu- 

Ite,  805. 
Hersciie..'b  star-gauges,  318. 
Hbrschkl  (W.)  states  that  tlie 
solar  system  is  in  motion  (1788), 
813. 
IlEHBCnELB  (W.)  views  on  the 

nature  of  nebula*,  805. 
HiFFARCHUs   discovers    preces- 
sion, 158. 
Hooke'm    drawings     of     Mars 

(1666),  384. 
Horizon  (celestial— sensible)  of 

an  observer  defined,  17,  30. 
Hour-angle  of  a  star  defined,  89. 
HnootNs'  determination  of  mo- 
tion of  stara  in  line  of  slglit, 
810. 
HuoaiMB  first  observes  the  spec- 
tra of  nebulte  (1864).  809. 
HuYOHENB  discovers  a  satellite 

of  Saturn  (1655).  353. 
HuTOHENB    discovers    laws   of 

central  forces.  116. 
Hdyohenb'  explanation  of  the 
appearances  of  Saturn's  rings 

(1656).  348. 

Inferior  planets  defined.  99. 

Intramercurial  planets.  336. 

Jahbocn  first  observes  solar  pro- 
minences in  daylight.  318. 

Julian  year.  184. 

Jupiter,  general  account.  340. 

Jupiter's  rotation-time.  343. 

Jupiter's  satellites,  348. 

Kakt'b  nebular  hypothesis,  838. 

Kkplbr'b  laws  enunciated,  109. 

Laplace's  nebular  hypothesis. 


Laplace's  investigation  of  tlie 
constitution  of  Saturn's  rings, 
252. 
Laplace's  relations  between  the 
mean  motions  of  Jupiter's  satel- 
lites, 248. 
Lassell  tliscovere  Neptune's  sat- 
ellite (1847),  260. 
Lassrll  discovers  two  satellites 

of  Uranus  (1847),  254. 
Latitude     (geocentric  —  geogra- 
phic) of  a  place  on  tlie  earth  de- 
fined, 8,  81,  41,  15t. 
Latitude  of  a  point  on  the  earth 
Is  measured  by  the  elevation  of 
the  pole,  81. 
Latitudes  and  longitudes  (celes- 

tlal)  defined,  95. 
Ijilitudcs  (terrestrial),  liow  deter- 
mined, 58. 
Le  Vebribr  computes  the  orbit 

of  melorlc  shower,  271. 
Lb  Verribk's  researches  on  the 

tlieory  of  Mercury.  236. 
Le  Verbikr's  work  on  perturba- 
tions of  Uranus.  357. 
Light-gathering  power  of  an  ob- 
ject-glass, 68. 
Light-ratio  (of  stars)  is  about  3.5, 

395. 
Line  of  colUmatlon  of  a  telescope, 

71. 

Local  time,  47. 

Lockybr'b  discovery  of  a  spec- 
troscopic method,  316. 

Longitude  of  a  place,  9,  10. 

I..ongitudo  of  a  place  on  tlic 
earth  (how  determined),  60. 53. 

liongitudes    (celestial)    defined, 

05 
Lucid  stars  defined,  389. 


^         - 


INDEX. 


t      V 


Luiur  plittMH,  nodei,  etc.  A« 
Moon'ii  phuHt'i.  node*,  etc. 

Mu«nlfyiiig  iK)W«r  of  au  eye- 
piece, M. 

Mujor  pUnoU  deflDetl.  191. 

Mure,  physlcul  (lewjripllou,  288. 

Man,  rot  itlon,  384. 

MursH  ialellUe*   dlHCOvered    by 

iiAix  (1877).  aaa. 

MA8KBLYNR  dotermliiw  the  den- 
sity of  tko  enrlli,  149. 

MaM  of  tha  BUD  in  roUtlnn  to 
miU8e«  of  planets,  167. 

Mean  aolir  limo  doflned.  45. 

Mercury'*  ntinospliere,  )a44. 

Mercury,  ll»  apparent  niotloua. 


Meridian  (celetllul)  defined,  27. 

Meridian  circle,  73. 

Meridians  (terreatrlal)    dcflnctl, 

27. 
Metonic  cycle,  188. 
Meteoric  showers,  26». 
Meteort   and   comets,  their  re- 

lation.  271. 
Meteors,  their  cause,  265. 
Milky  Way,  288. 
Milliy  Way.  its  general  iliape  ac- 
cording to  HEnscHEL,  818. 
Minor  planets  deflntd.  181. 
Minor  planets,  general  account, 

887. 
Mlra  Cetl  (variable  star),  296. 
Months,  different  kinds,  182. 
Moon,  general  account,  82a 
Moon'B  light  ttAw  o'  ^«  ■""' 

883. 
Moon's  phases,  188. 
Moon's  parallax,  161. 
Moon's  surface,  does  U  change? 
883. 


Motion  of  stars  In  the  line  of 

siglit,  810. 
Nadir  i)f  au  observer  detlneti,  18. 
Nuiitinil  uliuaiiac  dexcnbed,  "9. 
Nebulu!  uuU  clusters  in  geuund, 

804. 
Nebulu,'.  tlielr  i-pectra.  809. 
Nebular  liypolliesls  slaletl,  828. 
Neptune,   iliacovery    of,   by  La 

Veuuibh  and  Adamb   (1846), 

256. 
Neptune,  general  account,  256. 
Neptune's  satellite,  360. 
New  stars,  298. 
Nkwton  (I.)  calculates  orbit  of 

comet  of  1680.  280. 
Nkwtok  (I.).  Laws   of   Force, 

115. 

ObjcctWes,  or  object-glasses,  60. 

Obliquity  of  tlie  ecliptic.  91. 

Occultatlons  of  stars  by  the  moon 
(or  planets),  140. 

Olbebs's  hypothesis  of  the  ori- 
gin of  nsteroitls.  289. 

OI.BERB  pn-dlcts  the  return  of  a 
meteoric  shower,  269. 

Old  style  (In  dates).  185. 

Opposition  (of  a  planet  to  the 
sun)  defined.  85. 

Parallax  (annual)  defined,  68. 

Parallax  (horizontal)  defined,  66. 

Parallax  (in  general)  defined,  60. 

Parallax  of  the  sun,  161. 

Parallax  of  the  sUrB,  general  ac- 
count. 814. 

Parallel  sphere  defined,  88. 

Penumbra  Of  I  lit-  earth's  or  moon's 
shadow.  181. 

Photosphere  of  the  sun,  301. 

PiAZZi  discovers  the  first  asteroid 
(1801),  887. 


INDEX. 


887 


of  ulnra  in  the  line  of 
810. 

t  ttu  olMwrvordefliioti,  18. 
1  uiiniiiiitc  licHcnlwd,  *». 
and  ciuHleni  in  geuunil, 

,  llieir  i.pfclra,  800. 
•  liyputiieais  ttuled,  832. 
f,  liiscovery   of,   by  Lb 
iiBH  Hud  Adamb   (1846), 

c,  general  account,  209. 

e'8  MtLllite,  200. 

m,  298. 

N  (I.)  calculatea  orbit  of 

t  of  1680.  280. 

iM  (I.).  Laws   of   Force, 

Te»,  or  obJect-glaMe«,  60. 
lly  of  tlie  ccliplic.  91. 
ttions  of  stars  by  the  moon 
laneU),  140. 

a's  liypotlic8l«  of  the  orl- 
)f  nfitcroiilB,  289. 
a  prt-dicta  tlio  return  of  a 
lorio  sliower,  269. 
^1e  (in  dates).  185. 
it  ion  (of  a  planet  to  the 
defined.  85. 

IX  (annual)  defined,  88. 
i\x  (horizontal)  defined,  56. 
ax  (in  general)  defined,  60. 
ax  of  the  sun,  161. 
ax  of  the  stara,  general  ac- 
Dt,  814. 

el  sphere  defined,  28. 
nbra  Of  I  lit  earth's  or  moon'a 
dow.  181. 

tsphere  of  the  tun,  201. 
!i  discoven  the  flrat  Mteroid 
»1),  387. 


Planeta,  tlieir  relative  size  oxhib 

Itod,  191. 
Planetary  uebul«B  defined,  806. 
Planets;  seven  bodies  so  called 

by  the  ancients,  81. 
Plancto,  their  apparent  and  real 

motions,  96. 
Planets,  their  phyalcal  conatltu- 

liun,  261. 
Poles  of  the  celestial  sphere  de- 
fined, 21. 
PomUiKT'a  measure!  of  iolar  ra- 

dUtion,  205. 
Practical  astronomy  (daflned),  78. 
Precession    of    the     quinoxes, 

158. 
Prime  vertical  of  an  obaerrer  de- 
fined, 19. 
Problem  of  three  bodies,  119. 
Proper  motiona  of  stars,  812. 
Proper  motion  of  the  sun,  813. 
Ptolemt  determines  the  solar 

parallax,  166. 
Radiant  point  of  meteors,  370. 
Radius  vector,  107. 
Reflecting  telescopes,  66. 
Refracting  telescopes.  60. 
Refraction  of  light  in  the  atmos- 
phere, 169. 
Resisting  medium  in  space,  981. 
Reticle  of  a  transit  inatrumen*, 

71. 
Retrogradationa  of  the  planeU 

explained,  100. 
Right  aacensitm  of  a  star  defined, 

40. 
Right  ascensions  of  stars,  how 

determined  by  observation,  72. 
lUght  sphere  <u  (:■.'<  1,  39. 
ROBMBR    dhw.ux   'd    that    light 

moves  progitialvely,  176. 


noflSK's  measure  of  the  moont 

heat,  282. 
Harm  (I  lie).  140. 
Baturu,  gunoial  account,  246. 
Saturn's  rings,  248. 
Saturn's  satellites,  252. 
Seasons  (tlic),  02. 
SiiX(;hi,   on    solur   lonipcnUtire, 

206. 
Semidiametcrs  (apparent)  of  ce- 
lestial objects,  59. 

SexUut,  76. 

Sidereal  time  explained,  48. 

Sidereal  year,  158. 

Signs  of  he  Zodiac,  90. 

Solar  CO  ana,  etc.    8u  Sun, 

B<  '.ar  corona,  extent  of,  318. 

B')lar  cycle,  180. 

Boiar  heat,  its  amount,  204. 

rViiar  moti'.    in  sp    -3,  813. 

Solar  pare  irix,histoiy  of  attempt* 
to  d^'n  u.aelt,  165. 

Bclar     miallax   probably  about 
3' -81, 168. 

£/»)ar  prominences    .t)  gaseoua, 

Solar  system,  description,  190. 
Solar  system,  its  future,  220. 
Bohu'  temperature,  206. 
Bolsticea,  04. 
Spectrum  of  Solar  prominences, 

314. 
Spectrum  of  Solar  corona,  216. 
Spectrum  of  Mercury  and  Venus, 


Spectrum  of  Nebulae  and  Clus- 
ters, 809. 

Spectrum  of  fixed  Stars,  809. 

Spectrum  as  indicating  motions 
of  stars.  810. 

Star-clusters,  308. 


.uMjjiWtftfWWrf^-fr^^-^***"""'^"**'^'''^^^'^'*^' " 


|1! 


338 


INDEX, 


Star-gauge*  of  Hbrbchet.,  818. 
Stars  had  special  names  8000  B.O., 

291. 
Star-magnitudes,  290. 
Stars  of  various  magnitudes,  how 

distributed,  294. 
Stars  —  parallax   and    distance, 

814. 
Stars  seen   by  the   naked   eye 

about  2000,  291. 
Stars,  tlieir  proper  motions,  SISL 
Stars,  their  spectra,  810. 
Strutb's  (W.)  parallax  of  a^)ha 

Lyrm  (1888),  816. 
Summer  solstice,  88. 
Sun's  aiqwrent  path,  88. 
Sun's  constitution,  217. 
Sun's  (the)  existence  cannot  be  in- 

definitely  long,  220,  825. 
Sun's  mass  over  700  times  that  of 

the  planets,  194.' 
Sun,  physical  detKripUon,  900. 
Sun's;  proper  mption,  812, 
Sun's    rotation-time    about    25 

days,  200. 
Sun-spots  and  faculse,  200,  20S. 
Sun-qrats  are  confined  to  certain 

parta  of  the  disk,  206. 
Sun-spots,  their  nature,  209. 
Sun-spots,  their  periodicity,  211. 
Superior  plaoets  (defined),  99.      . 
Bwbdenboro'b  nebular  hypiotbe- 

sis,  828. 
Swift's  supposed  diacovetj  nS. 

Vulcan,  226. 
Symbols  used  in  astronomy,  11. 
Telescopes,  their  advantages,  ML 
Telescopes  (reflecting).  60. 
Telescopes  (t^racting),  6(K 


clb 


Tkmpel's  comet,  its  relnlion  to 

November  meteors,  272. 
Tempomry  stars,  298. 
Tides,  126. 
Total  solar,  eclipses,  description 

of,  212. 
Transit  instrument,  70. 
Transits  of  Mercury  and  Venus, 

226. 
Transits  of  Venus,  168. 
Triangul'ation,  160. 
Tropica)  year,  154. 
Twilight,  172. 
Trcno  Bbahb  observes  new  star 

of  1672.  2iW. 
Vhiverial  gravitation  discovered 

byJIswTON,  121. 
Universo!    gravitation    treated, 

11& 
Uranus,  general  account,  268. 
Variable   and  temporary  stars. 

general  account,  296. 
Variable  stars,  theories  of,  209i 
Velocity  of  light,  179. 
Venus's  atmosphere,  224. 
Venus,  ita  apparent  motions,  221. 
Vernal  ^uinox,  87. 
Vulcan,  226.; 

Watsok's  supposed  discovery  of 
.  Vulcan,  226. 

Weight  of  9.  body  defined,  14& 
Wilson's  theory  of  sun-spots, 

210: 
Winter  solstice,  .89. 
years,  idifferent  kinds,  188. 
Zenith  defined,  17. 
Zodiac,  90,     : 
Zodiacal  light,  278. 


m 


'empel'b  comet,  its  relation  to 
November  meteors,  272. 
empomry  stars,  208. 
ides,  128. 

otal  solar,  eclipses,  description 
of,  212. 

raosit  instrument,  70. 
ransits  of  Mercury  and  Venus, 
225. 

ransits  of  Yenus,  168. 
riangul'ation,  160. 
lopica]  year,  154. 
wilight,  172. 

Tcno  Brake  observes  new  star 
of  1572.  2^. 

^niverial  gravitation  discovered 
byJ^^BwtoN,  121. 
niversol    gravitation    treated, 
11& 

ranus,  general  account,  258. 
ariable   and  temporary  stars, 
general  account,  206. 
ariable  stars,  theories  of,  200; 
elooity  of  light,  170. 
enus's  atmosphere,  224 
enus,  its  apparent  motions,  221. 
ernnl  ^uinox,  87. 
uloaa,  226.; 

rATSOifr's  supposed  discovery  of 
Vulcau^  226. 

^flght  pt  9  My  defined,  148. 
'iLBON's  theory  of  sun-spqta, 
210; 

Inter  solstice,  .80. 
ears,  different  kinds,  188. 
snith  defined,  17. 
)d|ac,  QO, 
idiacalHgbt.  272. 


>  »'JMlill»H..M^iMir«<»W 


